MarkT:
You will likely have trouble sending clock and data along long cables like that unless at a low data rate. Logic signals degrade over a few feet / metres and can lead to crosstalk, spurious glitches etc (remember these signals have rise and fall times of a few nanoseconds). I'd select quite a low clock frequency in the first instance, say 10kHz or so, and add 100 ohm resistors in-line before the inputs to each 595 (suppresses reflections). You may still have problems - experiment with one '595 and set of LEDs first.More advanced cures are adding an RC low-pass filter and a schmitt trigger gate to clean up the edges.
I still have trouble to make more than 16 leds to move. This is first problem 
Second, there is a possible problem with a long wires.
Is there another way beside 595 to control 25 leds with just few wires? somebody mentioned SPI control