To buy leds cob 42-48W 36-39 V 1200mA 3500k, and to cut costs, I want to use a 250W step up with a 24v 20A 250W switching power supply, if I connect 5 cob leds will the leds burn out?
It looks like you try to choose a wrong driver. Your power supply must have constant current output with current that is compatible with your COBs. Also I recommend to use AC-DC driver to plug it in your power socket directly.
And I must warn you: do not buy AliExpress leds, their real characteristics are far away from those they write. My advice is to buy Cree, Bridgelux, Citizen, etc. COBs and Meanwell driver.
Yes the amperage is much to high on the 20A side. 4 amps a diode is too much and You will "throttle" the diode. You will need a power supply rated @ 250W With 36v and a 5-6 amp current. The "24v" from the power supply you have will not be enough and the diodes will either not turn on or be be dim. This can be costly/time consuming and dangerous so be smarter and don't cheap out. The power supply you are using is simply not designed for the diodes in question.