$$p=5n-(3n+k)$$

The profit $p$, in dollars, from selling $n$ units of a certain product is given by the equation above, where $k$ is a constant. If 500 units are produced and sold for a profit of $625, what is the value of $k$?

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We are given the following information:

$$p=5n-(3n+k)$$ $$n=500$$ $$p=625$$

Substituting the values:

$$625=5(500)-(3(500)+k)$$ $$625=2500-(1500+k)$$ $$625=1000-k$$ $$k=\boxed{375}$$