MOSFET Switch Always On?
The heater load needs to go between the drain and the +12v positive supply, and a new MOSFET may need to be used.
Connecting the heater in this manner might have led to the MOSFET getting damaged the first time it was used (because it's connected in a common-drain voltage buffer configuration and hence must drop 7-ish volts across the channel when the gate is driven to 5 volts). Even if it were only drawing 5 amps when in this configuration, that's still over 30 watts which probably led to catastrophic overheating of the transistor; That overheating likely caused it to now be short-circuited internally.
Also, be sure to double-check the source and drain pins -- if they are backwards, the body diode of the MOSFET will always conduct.