This is another example of a problem that can be solved by looking at the difference of the numbers and their ratio.

Once $50$ people go home from the stadium, how many more people are watching the game on TV than there are people at the stadium? At this point we know there are $5$ times as many people watching the game on TV than there are people at the stadium, so there are $5 - 1 = 4$ times more people watching at home than at the stadium. Use this ratio difference and the actual difference to figure out how many people are at the stadium. Then use this number to figure out how many people are at home.