Let $p, q, r \in \mathbb{R}$. If $f(x) = px^{2} + qx + r$ be such that $p + q + r = 3$ and $f (x + y) = f(x) + f(y) + xy$, for all $x, y \in \mathbb{R}$. Then the value of $f(5)$ is.
$25$
$30$
$35$
$40$
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