From 24V to 5V DC voltage regulator

READ THE DATASHEET.
The Max input voltage for an LM7805 is 18V, not 24V so the heatsink isn't going to do squat.
You could use a power dropping resistor to dissipate 24-7.5=16.5 V at 1.5A = 25W. (24.75)

Rdropping = (Vin - VLoad)/ ILoad = 11 ohms
PRdropping = IRdropping x VRdropping = 24.75 W

Would it be better to use a switching dc-dc converter (like the LM2596) from ebay ? (probably)
Do you have time to wait for that to arrive ? (I don't know)
Can you use the resistor until it arrives ? (yes)