Is it possible to fill a square of side 68 with an equal number of squares of side 3 and 5?

This C++ program does an exhaustive search of all possible tilings of a 68x68 square using 136 3x3 and 136 5x5 squares.

After a 38 hours execution and more than 80 GB of RAM used, the answer is NO. Check output.txt to see how many configurations where tested.

It would be great to have a mathematical prove of why this is not possible, but I haven't found one so far.