A dodgy cable could certainly be causing the issue connecting your phone to your computer. The individual connections within the cable responsible for power are different to those responsible for data transfer. Could you borrow a working cable from a friend or family member?
Are you following the process documented by Apple
here? Note what they say about the fact then doing an Update will preserve data but a Restore will wipe it and attempt to restore it from a backup (assuming you have one).
I tried to press the home button and on off button at the top right of the phone but it doesn't go into recovery mode whilst connected to my Mac book pro and plugged into the usb 3 port with the frayed cable with green showing underneath the plastic overcast and green red and yellow wires showing below the green underneath the plastic over case. Ill take it to the apple store and see if they can attach a cable to it and see if it works then or maybe buy a charging/usb cable for the iPhone 5c. No one in my family has a similar era phone unfortunately, unless a iPhone 8 plus or iPhone 11 pro cable would work?
Do you have your iPhone configured to backup to iCloud? Try logging into iCloud on the web and see whether all your pictures are there. If your phone can't boot beyond the Apple logo, it will be very difficult (perhaps impossible) to extract any data stored on it.
I backed up the photos then present on the phone and the pictures I wanted I took them off onto my computer in august 2021 using apple support's help, there was a issue then again with storage full all my photo stream and all pictures in the photos app disappeared then as I deleted apps they started reappearing, I think it was because my iCloud photo or some setting in iCloud relating to photos or in photos relating to iCloud was switched on or something and they couldn't be uploaded to the cloud because my storage on my phone was full. I was told to switch off the iCloud photo mode. The issue is there are more photos I have taken since august 2021 and I don't know if I can retrieve them with apple supports help or apple stores help or a iOS fixing software like tenorshare ifixit, which is kind of worrying me. Also if my last WhatsApp chats save was in august 2021 also will I still get contacts and chats from after august 2021 on a new iPhone if I restore my chats and use the same account after downloading the WhatsApp app onto the phone do you know? I have 3 new chats and contacts since august 2021 but I don't know if they will be on the new iPhone if I get one and download the WhatsApp app. when you start the WhatsApp app for the first time does it connect to your old account and are all your contacts there from the time you last used it? also are all the chats there from the last time you used it or only the ones you saved to iCloud in a WhatsApp backup?
Apparently this is the case. WhatsApp will "stop supporting" iOS 10 and 11 after 24 October 2022, meaning that it will no longer be compatible with iPhone 5 or iPhone 5C. When your phone was working, did you receive a notification within WhatsApp along the lines of "WhatsApp will stop supporting this version of iOS after 24 Oct 2022"?
I didn't receive a message like that at all unfortunately, maybe it would have been sent to me in October perhaps?
As I understand it, you will not be able to send or receive messages from your iPhone 5C after that date. Whether you will be able to view old/existing messages isn't clear.
See
this page on the WhatsApp web site for confirmation that, "We support iOS 12 or newer".
Perhaps it's time for a new phone.