How much gold is in a 5 dollar gold coin?

Unless the coin is certified bullion, probably none. "Gold" coins are called such because of the resemblance and the traditional that coins were made of precious metals.

But...If you're referring to an old (pre-1933) US $5 coin, it contains about 0.26 troy oz. of gold.

If you're referring to one of the modern $5 bullion coins sold to investors and collectors, the denomination is artificial. These coins contain 0.10 troy oz. of gold.