You are paying for 1000 Mb/s down, and are getting 60 Mb/s down?
How are you measuring this? Where is that 60 Mb/s down being sourced from?
Start with a test of the local network equipment. Even if you are provided 1000 Mb/s down to your dwelling, if your local network or device can't sustain that, it's going to be unusable.
Since it's been brought up that the cable is non-spec, test before and after you replace it. It may have nothing to do with the problem. I agree that going beyond Cat-5e isn't going to do you a whole lot of good, especially if you buy a cut-rate cable anyway.
Use a utility like
iperf3 to send data between two local machines and see what your throughput actually is. This will be the best theoretical throughput available to you over your local network between these two machines. Of course, if one or both computers is a potato, you might get poor results.