Your sizing indicates you need about 25 watts of power for the LEDS (5V * 5A). A Buck converter is not 100% efficient; I generally use 80% as a rule of thumb, If they are greater fine. 25 watts *1.2 (efficiency of converter) = 30 watts so with the converter you will need 30 Watts. 30 watts / 12 Volts = 2.5 Amps. This tells us that any supply used must be able to supply 2.5 Amps or more at 12VDC, so your 5A device would be AOK!
If you can split the 5V power for the LEDs into several sections of lower amperage, you'll be able to
use a few low-cost LM2596 buck converter modules. A buck-converter rated at 5A or more output
is likely to be more costly