Answer
$c=5/3$.
Work Step by Step
Since $f(x)$ is continuous, then it is continuous at $x=5$; thus we use the property that $$f(5)=\lim_{x\to 5}f(x)$$ where
$f(5)=4(5)+2c=20+2c$
and
$\lim_{x\to 5}f(x) =5^2-c$
Hence, we get $$25-c=20+2c\Longrightarrow 3c=5.$$
That is, $c=5/3$.
