At this power level, and if an adjustable current limit is needed,it's not a good idea to use a regulator IC that includes the output stage. The more logical solution would be a circuit based on the LM723 or similar. That is a regulator chip and separate power transistor(s). At 24 V and 5 A chances are you need more than 1 transistor. Alternatively separate reference and OPs could be used instead of the LM723.
As for a power supply I would suggest to start with a smaller version (e.g 0.5 or 1 A) first. It's less magic smoke and less expensive parts - so it's better for learning.
For the current limiting, there are three options:
1) the supply turns off, once the current gets to high. So a kind of electronic fuse.
2) the current is limited to the set value and the supply chances over from a constant voltage mode to a constant current mode. This is how most lab ppower supplies work. So you can choose maximum values for voltage and current, usually only one these values active at any time.
3) use so called fold back current limiting: the current limited to a miximum level like before, but the current limit goes down as the voltage goes down. This method is used in may of the integrated regulators like 780x or lm317. Foldback reduces the possible power dissipation and thus allows more current with given power transistors / heat sink.