Understanding split up wire

I guess that is Voice device and those are 4 telephone lines. UTP cable is just used to reduce number of cables (to have 1 cable instead of 4).

Those are analog trunk lines need for whatever analog phone devices you may have: Fax, modem, etc...The EQ line is basically VOIP(SIP).

Could One of these wires could also be supplying the internet?

Can you clarify what is connected to what? That might help. The cable in ETH1 port, where does it go? And those other UTP cables  on the right, what are the connected to?

EQ line is coming from the wall. I believe that's the EoC.  The lines 3, 4 and five are going to the Cisco switch

1,2 seem to be dead since I don't see activity

I doubt you will see any activity on your CISCO Switch (Model # of Switch), because according your picture those are SHDSL lines. Do Ports 1,2,3,4,5 go into separate ethernet ports on the CISCO Switch or are some of the pairs combined in someway? Meaning are there 5 ports that are used on the CISCO Switch. Can you provide a picture of how these pairs are connected to the CISCO Switch?

Have you asked your provider for help? What kind of circuit have they provided? Does any of this work?

If I could, that would be the first place I ask.  Long story short, we are getting rid of them.  The scenario is that I am unplugging this device from the switch and bringing in new connectivity with a different provider for internet and hosted phones.  I just wanted to know what their equipment was doing when I unplug it.