Is it better to use discrete components or voltage regulators for a variable power supply?
The only linear voltage regulator IC I know of that meets your specs is the LM338. The TO220 package version is a reasonable price, but with a minimum input-output differential of 3 V the power dissipation at 5 A is at least 15 W, which would require a large heat sink. To work over the full 0-32 V range at 5 A with current limiting a tracking pre-regulator is essential.
For efficiency the pre-regulator needs to be a switching type, and the output tracking needs to be tight. Therefore I would look at making a pure switching supply that meets the spec, then consider methods of reducing noise on the output. This could involve a discrete linear pass element (bipolar or FET) controlled by an op amp, whose task is simply to reduce ripple with a low voltage drop.
Switching supplies generally have automatic protection against reverse current. If the supply needs to absorb reverse current without raising the voltage (eg. for powering a motor controller or simulating a battery) use a synchronous switching regulator with 'half bridge' output.
You might also consider providing an auxiliary low noise output using a fixed pre-regulator and lower current linear regulator IC. For example the LM317 can easily supply up to 12V at 1A with current limiting when powered from 15 V. This could be useful for bench testing projects that need multiple supply voltages (often the higher voltage supply would normally come from a battery or unregulated mains supply, so low noise is not so important).