jmc

The numbers in the last row are $50,$ $49,$ $48,$ $47,$ $46,$ so we want to find the sum $$5+6+15+16+\cdots +45+46.$$ The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms.

We first add $5+15+25+35+45$ by observing that the mean of these five terms is $25,$ so their sum is $25\cdot 5.$ Similarly, the mean of the five terms in the sum $6+16+26+36+46$ is $26,$ so their sum is $26\cdot 5.$ Adding these sums, we find that the original sum is $$25\cdot 5+26\cdot 5=(25+26)\cdot 5=51\cdot 5=\boxed{255}.$$