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

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:

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