Yes, what you're doing is fine, with 5V at the gate, the MOSFET will be biased fully on with low conduction losses.
I didn't mean to say that there would be a problem, just that you should be wary of paying too much attention to the threshold rating which is specified at a very low current: 250µA in this case. In other words, if you have a 1A load and put just 2V on the gate, it will get hot.
EDIT:
Below the saturation current, the actual current drawn will depend on the load, not the gate voltage, which is what you want.