Where are you seeing the 10mbps, on the status screen for the ethernet.
Most ethernet interfaces run at 1gbit unless you have older or cheaper equipment that can only run 100mbps.
If you are seeing 10mbps on the status screen it almost has to be a bad cable. You can check the setting in the PC to be sure the interface is set to auto. If you set it to anything else you run the risk of it getting confused since switches and routers tend to always run auto.
Some device will drop to 10mbps and half duplex when they can't figure it out.
I would try a new cable. Be sure to use quality cable there is lots of fake being sold. You want pure copper (no cca) with wire size 22-24 (no flat or thin cables). Cat5e is fine unless you can get cat6 for cheaper, it will not run any better.