5 channels at 5 amps each is 25a. If you use a single PSU cable with 3x Molex on it you could very easily have major problems, smoke, fire, etc.
Standard PSU cabling is 18 gauge, which is only good to ~16 amps. Some beefy PSUs use 16 gauge (very rare on Molex cables, more common on ATX24P, CPU/PCIe cables), but that's still only rated for 22a.
Cheap PSUs tend to use 20 gauge, which is garbage and good for a whopping 11 amps.
They say no splitters in part because the connector we call a Molex is rated for 11 amps maximum, the PSU side of the splitter cannot deal with the 25a required.
In short, use at least two PSU cables, and no splitters.