Start by using some decent cable.
If your customer is not willing to pay for a bit of decent cable, then try to spend some effort in educating him on why it is important. If that does not work then wash your hands of it and choose some other project to work on.
Some other things you can do:
Use a power supply with the highest voltage you dare to use on your CAT5 cable.
Higher voltage is less current, and therefore reduces voltage drop. I would at least use 24V, but you can go upto 48V without getting into trouble because of the high voltage itself.
CAT5 has 4 wire pairs, and you only need 1 pair for RS485. So you can put 3 conductors in parallel to reduce the DC resistance.
Put the power supply in the middle. This halves the distance (and thus resistance) from the power supply to the furthest end, and it also halves the current though the wire. So you reduce the voltage drop over the cable by a factor of 4.
You can use a bipolar power supply with local SMPS circuits. For example +24V and -24V for the power delivery, and then add a GND wire that does not have any (or a very low) current through it.
You can use two (or more) power supplies distributed over the cable. Make sure those power supplies act decent if connected in parallel (for example by adding diodes). With multiple distributed power supplies you can make use of the cable resistance as a mechanism to even out the loading of the power supplies.
And because it's a RS485 system, making your power supplies "smart" is a relatively easy step. Add a microcontroller to each power supply that can can report voltage and current of the power supply.
Also consider this:
If you have 24V on the same cable as your RS485, it's easy to damage stuff with wiring faults.
This can be prevented by adding TVS diodes to the RS485 transceivers (or use transceivers with dectent built-in TVS diodes) and combine that with PPTC's, that limit the current into these TVS diodes during a DC wiring fault.
Also have a look at this old, but very good application note:
https://html.duckduckgo.com/html?q=ten+ways+to+bulletproof+rs485