Drilling a cuboid

The surface area of the cuboid is $2[5(15)+6(5)+15(6)]=390$

There are three circles at the top and three at the bottom that were removed, and the total area is $6(\pi)(2^2)=24\pi$ .

We need to know the lateral area of the three cylindrical holes. We can use the formula, $A=ch$ where $c$ is the circumference of the base and $h$ is the height. So we have, $3(4\pi)(5)=60\pi$

The total surface of the new solid is surface area of the cuboid minus the area of the six circles plus the lateral area of the three cylindrical holes. We have

$390-24\pi+60\pi=$ $\boxed{390+36\pi}$