full-wave bridge rectifier -> 22.6 VDC -> Smoothed with 100uF Elec.Cap -> 23.999VDC -> 7805 Regulated -> 4.6 VDC -> Filtered 10uF Elec.Cap -> 4.9999VDC
It should have been more like (given an ideal transformer with a sine wave output):
24C AC -> rectified and peak rectified to 24*sqr(2)= 34V DC
which is all too much for a 7805!
You're probably overloading the transformer or it's bad, since you get that low a voltage reading (or you measured it wrong?).
You need a capacitor of (rule of thumb) minimum 2,000 µF/A (i.e. 4,000 µF minimum for a 2A supply)
2,000 µF @ a 1A current drain is around the pain limit regarding ripple voltage.
Using 4,700µF with your 1A supply wouldn't hurt
Do you know anything about what current the wall wart can supply?
(If the supply can only deliver 100mA, it's a bit too much expecting 1A after the 7805).
I have read that I can toss a L741 before the 7805 to help protect it. Which makes me wonder if I can(when i figure the dtasheets out) use a TLC272CP in its place.
Not really sure what you're getting at here?
"before", I read as, in between the transformer/rectifier and the 7805?
A power resistor to suck up and waste some of that power and drop the voltage would be the best protection.
If you're talking about a current limiter instead... Like a cat, that can be skinned in so many ways and op-amps of all kinds will come in handy for that.
But... Better start off by finding another wall wart given off, say, 6V to 9V (max.) if it's an AC output
(8V to 12V if it's giving off DC).
Or better yet... Make a small lab supply with variable voltage, variable current limiter and metering - that really ought to be one of the first projects for everyone starting out in electronics, since you just cannot live without it.
Batteries and ad hoc mock up supplies are poor solutions, even if you don't take your hobby too serious