24 volts times 5 amps means you can get a maximum of 120 watts from the transformer.
Careful -- you're correct up to here, when PF = 1. Otherwise, the general truth is 120 VA of capacity.
If the output is bridge rectified and connected to a capacitor you will get a maximum voltage of about 35 VDC, no load. Once you put a load on the output the voltage will drop and because of voltage drops across diodes, etc., you cannot expect to get the maximum 120 watts out. As a rough guess I’d say you might get 30 VDC at maybe 3 amps but an unregulated supply like this is of little use for a workbench supply.
A FWB rectifier, with cap-input filter, typically has PF ~ 0.5, so you should expect 120 VA * 0.5 PF = 60 W available output. About 2A DC would be reasonable.
Think of it as the price you pay for getting extra voltage out.

(Indeed, the price is even worse if you use a doubler, say. There, PF can be ~0.2.)
You can always run more, of course, either for higher operating temperature*, or for short durations since the temperature is effectively averaged over a long period of time (minutes?). A momentary load of 4 or 5A DC might be acceptable, say for CNC controller or audio amp applications, since the average will tend to be lower.
*Given suitable considerations. Like, will ambient temperature always be modest? Or is there a fan? Or is lower operating lifetime acceptable? That sort of thing.
Tim