You regulate the Peltier power supply voltage to regulate the current. PWM will not work to regulate the current.
If the Peltier is specified as 12V/5A, then it should draw 5A from your 12V power supply.
Best to check both with a multimeter, though, and check whether the power supply has a pot (possibly internal) to adjust the voltage.
- Display - 10V 2A
What sort of display draws 20 Watts?