My laptop does not recognize my "older" USB 3.0 Back-Up Drives (I have 2)

Are these drives recognized on other systems when connected?
If it works when connected to another system.
The  error might be a conflict in drive assignment.
When connected, check the device manager. Then check drive management to confirm whether the HD from the USB is seen and where the error lies.

check device manager for errors -  and lookup if they show up there when you connect them
so : open DM - then connect the drive

usual causes :
bad drive or , bad cable
error on usb device in Device manager ( check it)
since it is an older laptop - is it usb 2 or usb 3 you connect to, and what model s are the drives?
on usb 2 you may need external power for usb drives

If the data on there is critical, you can crack open the case and try mounting the hard drive in a desktop or get another case. Those things are just regular hard drives in a plastic shell with a little USB/power adapter attached. It's possible the connectors on the case are bad, or it's not getting enough power.

some have the usb integrated into the logic card of the drive - thus cannot be connected by sata

The asker has the WD Mybook which in the several cases was a green model drive within the 3.5" enclosure.

Hello..... Thanks all.
I spent several hours on this last night and just could not get things to work right.
Here is what is worth noting...…. I did see the drive ONLY in the device manager. It said it was working???
I discovered that if I installed the western digital software (downloaded it) and if I re-powered the computer between attempts - I saw "some" progress - but I still could not access the drive. One time only I saw the drive listed in the "file explorer".
The western digital software had tests I could run, it passed the first few but the most important one it failed.
I finally gave up and decided to just go buy a new drive for my backup.
I will still consider suggestions but I think one part of the hardware is broken (cable, power supply, or drive itself).
Thanks Again!!!!!!!!

sometimes when a person is impatient for the system to recognize a device and nothing happens right away they unplug the usb cable and plug it into another port before the drivers are finished installing behind the scenes, then you get the error that the drivers failed to install for your device.  when you plug in a device into a usb ports whether it is a webcam, keyboard, mouse or external drive or usb stick, windows has to install drivers for that particular device and until the drivers are installed the device will not be recognized. If you unplug the device before windows can detect the device, search for drivers and install them, then the device is going to have problems every time you plug that device into the same usb port.  Drivers are tied to each individual usb port. If you dont believe me try plugging  your keyboard into another usb port and the keyboard will not work for a few seconds or more until windows locates drivers for the keyboard and ties it to this specific port. Often windows will keep registry keys associated with devices previously plugged into that port, this is so that you dont have to continually wait for windows to identify the device, look up drivers for it, and then install the drivers.  But a partially installed driver corrupts the registry as it is only partially uninstalled, often a restart of the computer will resolve this issue as this registry key may be removed other times you can use a usb registry cleaner tool that will remove corupt or obsolete registry keys. One tool is is called usboblivion. and can be downloaded from here: https://sourceforge.net/projects/usboblivion/   I have resolve scores of usb detection error issues with this tool over the last several years and keep the tool in my usb tool box.  This application is a self executable file and does not install on the computer. You must run it as an administrator and check "do a real clean" as the default will just run it in test mode...  the program saves a reg file so you can undo changes made to the system registry. I never had to use this recovery file to undue changes.. and I am sure I used the application at least a hundred times on various systems.

You must always check your backup disks when you move from system to system.  A backup that is not checked is just worthless.

5 years is a long time.  The disks may have failed from lack of use.

Even in storage, you should be checking that disk periodically and, if you want to keep the archived data, preparing a newer disk to copy the data to it.

Backups must be checked to be certain it's reliable.

you can also check with disk management, and check if the drive is seen there, and has a drive letter
you can give a drive letter when it's missing