To answer your question you need to know how much current the relay pulls when energised, and what gauge cat 5 cable you are using.
Armed with this information you will be able to work out the volt drop of the cable for the length of run you have.
You could probably expect 7ohms per 100ft of resistance for most cat 5 cables.
So we have 130ft at 7ohms per 100ft = 7*1.3 = 9.1. so the total resistance is 9.1 ohms. Let's say the relay pulls 500mA, that will give you a volt drop of 4.55V. (Ohms law E = IR, or Volt drop = 0.5 x 9.1). The voltage availiable to the relay will be 24 - 4.55 = 19.45v, is that enough for your relay?
The above is for an illutration only, you need to find out the exact figures.
Paul