$p$ and $q$ are prime numbers so that:

${p}^{3}-{q}^{5}={(p + q)}^{2}$ .

Find $p + q$ .

The answer is 10.

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I seriously got it my first time. I plugged in $p=7$ and $q=3$ . In fact... wait a second. I posted this problem here . Great minds think alike! I came up with it in the back of math class. :O