iMac Running Very Sluggish

1) State type of drives you have in your iMac - mechanical disk or SSD disk, also if you have an internal CD/DVD drive.

Heat causes kernel_task to eat up all available CPU cycles attempting to reduce CPU usage.

2) Also run top or activity monitor + mention if kernel_task shows up using a CPU all the time.

This will show if kernel_task is the culprit.

3) If a Chrome task shows up as highest CPU user, this is likely Flash ad, so just kill the offending thread using the Chrome task manager.

4) If your machine is swapping (top shows this), then evict processes from memory by killing off unused processes.

5) If you have lots of disk space + many small files, you may see mds_* processes eating up many CPU all at once... for a very long time...

The fix for this is a bit complex, so just say if this is the problem, before I provide details of this fix.

You probably have a 5400 RPM Hard Drive on the iMac which is much slower than the SSD newer Macbooks. Adding RAM will help some and so will replacing the Hard Drive with an SSD. And maybe it's time to consider upgrade options.

Also, the GPU memory sharing is consuming RAM and taking away from your other applications. A separate GPU with additional separate memory will further free up more RAM for your applications.

Browsers are memory hogs (especially Chrome). Besides Chrome and Safari, what other browsers are you running? How many windows and tabs are open? I usually have no memory problems when using less than 20 windows and tab with just Safari. Chrome is noticeably slower for me, and running both will further slow down your Mac.

BTW, check your Hard Drive with Disk Utility to see if there are any errors. If it's very poor performance, it may be more than just running out of memory and could be a sign of a failing hard drive.

02:
Which specific Model iMac is it?  https://support.apple.com/en-us/HT201191

Is it this one?
https://support.apple.com/en-us/HT201191#1a
https://support.apple.com/en-us/HT201191#install1
You can go up to 32 GB, and you can buy up to 3 sticks of  8 GB RAM for that model.

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01:
Until you get the RAM and/or SSD updates to speed up the iMac, you need to run the activity monitor and identify what's slowing you down.  
Even with SSDs, you don't want to swap.  It's still slower than RAM.

If you have lots of cached RAM after you quit he programs, you should also run:
sudo purge
It will prompt you for your admin user password.  This will clear the cached portions of closed software, and free up some space so you don't swap quite as soon.  I used to run that constantly on Mavericks to keep my system from swapping so much and slowing down noticeably.

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Additional Info (My slight rant)
If you're on Mavericks, you should upgrade to a newer OS X, at least El Capitan.  Mavericks was the first non-cat system and seems to be the buggiest and most bloated of the newer era OS X.

8 GB is only really enough for a Casual user.  If you are running lots of apps or something heavy hitting, you've really needed 16 GB since Mavericks.  I would have benefited from 24GB on Mavericks, 20 GB on El Capitan, but stupid Apple only had 16 GB Mac Book Pro Models.  Since Sierra, I could work within 16 GB.  8 GB is only for the home user that just surf the web or watch videos.  While it works for most users, 10-12 GB would be better for many of them.

Lion worked on 4 GB for light users, but really needed 6-8GB for power users, same as Mountain Lion.  They've always sold underpowered Macs for the casual user.  Those are what they keep in stock.  If you want a more useful Mac with more RAM, better CPU, and/or better disk capacity,  you have to order and wait.  Stupid Apple.

I'd second what @serialband says.

It is super easy to replace or add extra RAM in an iMac from 2015.  Use a website like crucial.com or crucial.co.uk and enter the exact model of Mac and it will present all the options .. getting up to 16GB or more will make a difference.

Replacing the HD with an SSD will make a bigger difference but will cost a lot more relatively speaking and if you're not a heavy user you may notice it less after the RAM upgrade.

If the iMac is left running for longer periods it will execute all the cleanup scripts automatically anyway .. using the Mac for an hour here or there and leaving it switched off the rest of the time MAY mean that some scripts don't execute but OSX is not very prone to such issues until the HD is 90%+ full.

In summary ... Upgrade to the latest OSX version (if you're not on 10.14 already) and add at least 8GB of RAM to get to 16GB.

Thanks all. I won't be back in the office for a few days but I will run the activity monitor when i'm in... I did do that before and it was the browsers that was taking most of the memory.

I will order some RAM now. I see my iMac has 4 slots:

01 - 4GB
02 - 4GB
03 - empty
04 - empty

What is the max setup that I can have? Can I go 8 + 8 + 8 + 8 = 32GB

Also, where is the best place to buy RAM... I haven't bought or added RAM since my Windows days :-)

I use Crucial for RAM - https://www.crucial.com - https://uk.crucial.com - https://eu.crucial.com

If you put in the proper model in their website it'll tell you the MAX RAM it can handle .. usually paired so 2 X 8GB added to the 2 X 4 would give you 24GB and the difference between having 24 and 32 would be negligible and you'd be saving throwing away 2 x 4Gb.

Ok great, thanks Eoin

Be aware that going to High Sierra or Mojave means changing the formatting of the disk to APFS.  This will make the disk unreadable to older OS X.  Sierra stays on HFS+ and supports reading APFS disks.  If you have numerous older systems to support you may not want to upgrade past Sierra until you're ready to get all of them over to at least Sierra first.  If you don't then it doesn't matter.
https://www.techrepublic.com/article/apfs-vs-hfs-which-apple-filesystem-is-better/

Being an older system, I wouldn't buy more than needed.  You'd only extend the life of the system somewhat.  If you're a light user, just get a single 8GB stick.  Check your Activity Monitor to see how much you need when you run everything that you normally run.  Don't buy extra.

Once you have enough RAM, more RAM won't really speed things up anymore.  It just lets you run more programs at the same time.  The next upgrade would be the SSD if you just have a spinning HD.  That would double your apparent speed.

You don't have to actually swap out the internal disk.  You can just get a external USB 3 disk and attach it, install a new OSX, and set it as the default boot disk.  You can keep the internal disk as a data disk.  That would make it an easier and cheaper upgrade.  External SSDs are cheap enough.

Macs have been able to boot from external disks for quite some time now.  The nice think about Macs is that it's all compatible and you can easily move that external boot disk to another system and it boots just fine.  Basically, anything starting from around the Core 2 to now will work on the same boot disk.  It won't work if it's between an older generation model not supported by the OS, however, within the older generation models you could do the same thing.  I used to do that with Tiger on the older PowerPC Mac systems.  Windows can't do it as easily since there's so much more different hardware to support.

Tip: Better to know than guess.

For example, top will tell you if you have a memory shortage.

Best to determine the exact source of your problem, then you'll know how to fix the problem.

Likely areas to check - swapping + heat causing kernel_task to spin + other CPU spinner.

So top is your best starting point to find swapping + CPU problems.

Activity Monitor works better than top for the Mac.  Even if you are a command line guru, Activity Monitor is just easier to navigate and easier to visualize.

Correct Activity Monitor is better than top + with top, many times, it's easier to pick out gross problems quickly.

I always reach for top first, then Activity Monitor.

I always reach for top first, then Activity Monitor.

You're a linux guy, not a Mac guy.