Hi Clemson,
Your 12V supply requirement certainly makes a big difference to the design of your amplifier. As I said earlier, to get 5W into 8 ohms, you need nearly 18V p-p, which is not normally available from a 12V supply.
Therefore you need two amplifiers, connected in a "bridge" configuration, where one amplifier drives one of the speaker wires and the other amp drives the other speaker wire with reversed polarity, effectively doubling the voltage across the speaker. Car radios do it this way.
There are many dual amplifier ICs available that will easily give 5W bridged into 8 ohms. They are not opamps, are they allowed? You could always design your own dual amplifier with 2 opamps and 4 darlington transistors, if you must use opamps. The amplifier ICs and opamps with transistors are analog and are therefore inefficient, so will need a heatsink.
If allowed, I would go "high-tech" and blow away the instructor and the others in the class. I would use one of the latest "class-D" audio power amp ICs available from Texas Instruments. Their TPA3001D1 provides about 6.5W into 8 ohms at low distortion when operating on a 12V supply. With its 85% efficiency, it doesn't need a heatsink. However, like most modern electronic parts, its package is surface-mount, so its 24 pins are very small and crowded. It would take good skill to solder the thing. Check the datasheet and see if you can get a sample IC from TI:
http://www-s.ti.com/sc/ds/tpa3001d1.pdf