Maximum cable length between Raspberry and a 5V WS2812 led strip
There are many answers to this question.  Some rely on starting over with good requirements.


(As already stated) Thicker wires offer less resistance. Also CAT5 is a twisted pair cable and is best used to transmit balanced signals, not digital logic signals.
Remote power supply for LEDs.  Why not only connect data and ground back to the controller.  And provide power to the LEDs local to the LED.  Thicker wires are not as necessary as the current will be reduced. But caution will need to be taken to prevent ground loops!!!
Consider buying LED strips with less demanding timing requirements.  The strips you specify require signals with nanosecond accuracy.  There are strips with separate clock and data lines which are likely more tolerant.


added later...


Arduino boards are small.  Consider locating the Arduino board closer to the beginning of the LED strip.
Avoid powering the LED strips through the Arduino's own 5 volt regulator (if you are using 5 volt parts).  Instead use a heavy duty (several amps) regulated 5 volt power supply and connect the LED power lead to the 5 volt regulated power supply.