Just use a 9 volt battery and a 7805 regulator.
- You can get a 7805 from wherever you got your logic ICs. Other regulators aren't as commonly available, and other regulators aren't as forgiving as the 7805 (it isn't picky about the surrounding circuit and is pretty rugged electrically.)
- 9 volt batteries can't deliver enough current to burn things out if you wire something wrong.
- It is easy to tell when to replace the battery - when the 7805 output drops below 5V.
Simple and reliable is best if you are just beginning.
I mean, consider what happens if your circuit doesn't work.
If you are using one of the "better" regulators, then they can oscillate if the circuit (input and output capacitance) is wrong. The output voltage will be wrong (and vary thousands of times a second.) How will you find that as a beginner?
If you use a stack of 1.5V batteries, how will you be sure that you didn't get more than 5V long enough to damage something?
- Only power the circuit when you are using it (saves battery power.)
- Use a new battery when you go to demonstrate it to your instructor.
- Buy a bunch of 100 nanofarad capacitors when you buy your 7805. Place one 100nF capacitor across the power supply pins of every IC in the circuit - right at the IC. Everytime a digital IC switches states, it draws a spurt of current. That can cause the voltage at the IC to dip, which can cause the IC to misbehave. The capacitors make up for the little spurts and keep the voltage steady - your circuit will be more reliable. These are known as "decoupling capacitors."
- If your circuit doesn't work, you can touch the ICs with your finger. If any IC is noticeably warmer than the others, then you can start looking for wiring problems around that IC. A 9 volt battery can deliver enough current to make things get warm, but not enough to burn your finger (or go bang.) The AA 1.5V cells can easily deliver enough current to burn a finger or worse.
- Build your 5V regulator circuit by itself first, and make sure it delivers 5V before you attach any of your logic ICs to it.
The other answers give good advice in general, but you are a student just starting out. Simple and reliable are more important than any other considerations - for now.
As you go further into electronic things, you can look into more sophisticated regulators or other batteries.
For now, do what always works and has a very low chance of going wrong - you aren't yet equipped to deal with problems.