What parameters are to be considered when choosing a MOSFET?
All the parameters are important in one situation or another (that's why they're on the datasheet!). In this case you have a (presumably) slow-switching circuit that is either on or off. 

The first ones you should look at are the drive voltage to switch it on (in the case of the IRF740, 10V is required, so it's unsuitable for direct logic drive). Look at voltage rating. Higher voltage rated MOSFETs will tend to be more expensive and/or have higher on resistance for the current. The IRF740 has a 400V rating. If you only have a 12V supply so that 25V or 30V rating is plenty, then you're leaving money (or silicon) on the table by using an unnecessarily high voltage rated part that probably runs hotter than some alternative. 

Then look at the Rds(on) and thermal properties to estimate how much power it will dissipate when turned on (and therefore if a heatsink is required, and if it is required, what the thermal resistance to ambient needs to be). 

In the case of the IRF740 it has a Rds(on) with 10V drive of 0.55 ohm, which increases to maybe 50% more at high junction temperature. So call it 0.83 ohm. At 5A it will dissipate 20.6W, requiring a large heat sink or heat sink and fan. 

If you use a 25V MOSFET such as a PSMN0R9 you can drive it with 4.5V and it will have 1m\$\Omega\$ Rds(on) with 10V drive or 1.25\$\Omega\$ with 4.5V drive (with a similar temperature effect). Assuming 1.9m\$\Omega\$ that's power dissipation at 5A of less than 50mW and it won't get warm even without a heat sink (so the Rds(on) will actually be quite a bit lower again). 

There are other effects when you try to switch the MOSFET quickly (gate charge) and so on, but the above-mentioned are probably the parameters that you should look at initially in your particular application. 

And, of course there are practical considerations such as package, cost and availability and part status (active vs. obsolescent) if you're going into production.