Linear convolution of discrete signals with defined lengths

What is the maximum count of non-zero elements, that can a linear convolution of discrete signals of "lengths" 5 and 7 have?

When I label the length of signal $x[n]$ as $M$, and the length of signal $h[n]$ as $N$, then the length of their convolution is the signal $y[n]=M+N-1$. However this is not that thing I was looking for. So how can I find the maximum count of non-zero elements?