You're not going to find a classic muscle car in any kind of halfway decent condition for $5K. Those things tend to go for really crazy money, not to mention that for most people a decades-old car is not necessarily the best thing for a daily driver.

Here's a pretty typical example:

https://barnfinds.com/45k-mile-1965-chevrolet-chevelle-malibu-ss-convertible/

That’s a tough one. 

There are reliable muscle cars, but they aren’t cheap. 

There are cheap muscle cars, but they aren’t reliable. 

And then there are reliable cheap cars, but they aren’t muscle. 

Pie in the sky.

Reliability and Muscle rarely belong in a same sentence for a used car, to be honest. You may be able to find an older generation Mustang, but chances are it has been through rough driving being a muscle car itself. Don't bother to look at used Dodge Chargers and Challengers. Besides being notoriously famous for unreliable, all of the used ones had been through abuses. For a budget under 5k and especially in this market, your chances are slim unless you can find a private sale. All car dealerships are on the used-cars-are-more-expensive-nowadays bandwagon.

5k isnt much, its gonna be hard to be honest. Any classics worth having are going for way more than that. Id avoid most cars from the 70's, alot of rust buckets depending on where youre from. Some late 90's - early 2000's 4.6 mustangs are pretty affordable and have a good sound, but thats kind of it. Probably dont want to hear this, but the V6 camaros/mustangs are cheap, and can often hold up pretty well. A V6 isnt a muscle car, but often more practical depending on where youre at in life. Realize any used muscle car is, well a used muscle car. 95% chance that the thing was abused/ragged on. So make sure you have a good set of eyes look over this thing. 

Back when I was in highschool (2015), I found a 3.8 V6 camaro, 66k miles for $2700. I put almost 10k miles a year on it & its held up well. Yeah people would tell me its a V6, but cmon, anyone know those things understands why it still runs. 

Here's a classic muscle car with bids currently just under $5K (though granted they may go higher). Gives you an idea of what you can expect for that kind of coin:

https://barnfinds.com/fc7-in-violet-in-ruins-1971-plymouth-cuda-340/

Find a New Edge style V6 Mustang, the 1999-2004 Era. They are reliable enough. A college friend of mine has one. He got it in 2009 as a high school graduation present with around 80,000 miles. He's gone from living in Cincinnati to Baltimore and St Louis with that car and he DDs it. It's well over 200k miles at this point. Find a low mileage one and replace the rubber stuff under the hood. I disagree with nta98, V6 Mustangs are still pony cars. They're faster than the run-of-the-mill sedans of their eras. 

NTA makes a good suggestion: V6 instead of V8.

Other options to save $:

• Look for "sister cars", like Mercury Cougar instead of Ford Mustang
• Look for less-desirable cars of the same vintage, like Chevy Nova instead of Chevelle
• Look at 4-door sedans instead of 2-door coupes
• Non-numbers-matching
• Learn to love the "survivor car" aesthetic

At that price, though, you're likely gonna be talking project cars.  Be prepared to do some body, electrical, & engine work.

If you locate a classic muscle car for 5k, you would probably need to put 20k into it.

Unfortunately, I don't there is anything that exists in that price range that would fulfill what you are looking for.

Ok

1. 3rd and 4th generation mustangs

2. 4th and 5th generation Chevy El Caminos (Not sure if you'd consider that as a muscle car but I think it counts)

3. 3rd and 4th generation Camaros

4. Mid to late 70s muscle cars in general (Get while the prices are still low)

5. 3rd and 4th generation Pontiac Firebirds

Whatever you choose, make sure to really check it out to see what you're actually getting, don't make my mistake and buy something that needs $1000 in work, good luck.