Designing a voltage follower that can provide up to 5A of current to a load
This is a good start, but it needs a few improvements.  Op-amp voltage followers work because they compare the output voltage to their input voltage.  In your circuit, however, the feedback is being drawn from the gate of your BJT.  So, you'll see the output voltage across your load somewhere between 0.3 and 0.7 volts less than your input voltage.  By using the emitter voltage as feedback, the op-amp will output a slightly higher voltage to compensate for this.

Another improvement deals with current handling.  A BJT transistor usually has a current gain between 10 and 150 times.  So, in a worst case scenario, the op-amp may be required to source up to 0.5 amps.  We can do better.  If you replace the single transistor with two transistors configured as a Darlington Pair, you get much higher current gain.

As for power dissipation, make sure you use a power transistor.  Find the maximum power you expect to dissipate in the transistors, and double it, as a rule of thumb.  Power transistors are designed to dissipate that much heat.  Smaller BJTs are not.