Do what I said and use one one adjustable flyback converter with a center-tapped transformer to produce your two bipolar voltages 0 to +/-15V at the same time, and use an adjustable buck converter to produce your 0-5V.
To power these two DC-DC converters, use a "step-down transformer+rectifier+ smoothing capacitor" that produces around 7VDC or so from the AC main voltage. It's not too important what this voltage is, but it has to be higher than "5V+buck converter drop out voltage" (not ridiculously higher than though since this makes it inefficient and hard to build). It is also preferable to have the rectifier output voltage somewhere in the center of the 0-15V range (for best performance of the flyback converter). This will need two transformers.
THe simplest way to only use one transformer (the AC main stepdown transformer) would be to use 3 separate converters. The rectifier output voltage would be higher than 15V+dropout voltage for all the converters, and you would use two buck converters to generate 0-5V and 0-15V, and a buck-boost converter to generate your 0 to -15V. Obviously, your bipolar voltages won't be automatically equal in this case since two different converters are making them.
THe other simple one-transformer method is you could also design the transformer-rectifier to produce a +VDC and -VDC voltage that is high/low enough for positive/negative linear regulators to work (due to their dropout voltage) and then regulate them will adjustable linear regulators to produce 0-5V, 0-15V, and 0 to -15V. Positive linear regulators used on the +VDC rectifier output to produce your positive voltages while a negative linear regulator is needed on the -VDC output to produce your -15V. But this is inefficient.
There are other ways to do it with only one transformer (mainly adjusting the rectiifer output voltage higher or lower than the required DC-DC converter output voltages and picking different kinds of DC-DC converters to use)...but they are overcomplicated.