The IRF3205 is not logic level so you can't expect it to switch with 5V - it's spec'd for a minimum of 10V gate voltage.
The only important specs of a switching MOSFET are voltage and the Rds(on) value and the Vgs value that goes with it. In most cases I've seen the maximum current is simply the maximum power rating with infinite heatsink (recast as a current value). Unless you are providing water-cooling you won't be running at anything like that current!
A 12V 50W halogen will take about 4A steady state, so for less than 0.25W dissipation (no heatsink required), you'd choose Rds(on) of 15milliohms or less. Here the IRF3205 is fine (so long as you drive it with 10V or more).
So clearly you are either failing to provide 10V drive, or your circuit is wrong (using source-follower rather than common-source configuration perhaps?)