Hi, I had a similar problem and here's what I think I know:
I think you are lucky you have radio interference instead of static.
You need to find out if it is a balanced or unbalanced mic. Balanced is basically 2 wires plus a shield and unbalanced is one wire and a shield. Its most likely unbalanced. If it is unbalanced you can't run it more than 10 or 15 feet without interference.
Also, ground the shield only on the amp side and leave the other end free. I don't know about using CAT5 wire for mics, but I read in this forum that people use it for that a lot on security camera mics--if it is shielded it should work.
You may want to try reversing the polarity of the wires or trying different pairs. If that fails, get some shielded 18ga 2 strand wire at home depot and solder the connections--be careful that the hairs on the shield are not where they shouldn't be. Use an ohm meter to check for shorts between the three wires.