I'd say to delete both resistors no matter which 555 you are using.
The IRF520 has a listed Rdson of 0.27 ohms with Vgs = 10 V. Even if you had 10 v of gate drive (which you don't), the transistor would be dissipating over 1 W, enough to get pretty warm.
If your circuit is pulling only 2 A through the LEDs when it should be 5 A, that indicates that the FET is not fully enhanced, fully on. In this case the voltage across the FET, Vds, probably is not down around 1.3 V, which is why the FET is overheating and the load current is only 2 A. You can verify this by measuring the voltage across the LEDs. If it is less than around 10.5 V, you're probably starving the FET.
ak