Suppose $f(x) = \frac{x}{5} + 3$ and $g(x) = 4-x$. If $f(g(a)) = 5$, find $a$.
To do that, I can start by plugging in $g(a)$ into $f(x)$ and simplifying. So, $f(g(a)) = \frac{g(a)}{5} + 3 = \frac{4-a}{5} + 3$. Subtracting $3$ from both sides, I get $\frac{4-a}{5} = 2$. Multiplying both sides by $5$, I get $4-a = 10$. Subtracting $4$ from both sides, I get $-a = 6$. Dividing both sides by $-1$, I get $a = -6$. This is the value of $a$ that makes $f(g(a)) = 5$. 