jmc

The total number of books in the warehouse is $1335\cdot 39$. If Melvin packs $b$ boxes of $40$ books each and has $r$ books left over, then $1335\cdot 39=40b+r$. Thus, what we are looking for is the remainder when $1335\cdot 39$ is divided by $40$.

We note that $39\equiv -1(\mathrm{mod}40)$. Therefore, we have $$\begin{array}{rl}1335\cdot 39& \equiv 1335\cdot (-1)\\ & \equiv -1335(\mathrm{mod}40).\end{array}$$Now we note that $-1335=-1400+65$, and $-1400$ is a multiple of $40$. Therefore, $-1335\equiv 65\equiv 25(\mathrm{mod}40)$, which implies that the remainder is $\boxed{25}$ books.