All of that slack with the wires so close to each other will be bad for your Ethernet. Going to need to terminate those cables again with shorter stick out.
Yes it does look like at least cat5, if they hadn’t painted it it would be easier to see.
In the building where I work they only used rj45 jacks in the wall plates. One was labeled voice, the other data. They did use cheap phone cable for the voice lines though.