A gambler plays roulette 400 times staking $1 on red each time.What is the chance that he will win at least $5?

First you need to define the roulette wheel. Presumably it has 36 paying numbers 1-36 but there is also at least one and maybe two house numbers 0 and sometimes 00 (the latter being an "American" roulette wheel). Whether there are 37 or 38 numbers on the wheel will affect the probability and without knowing this you cannot answer this question. Note: 0 and 00 are green, neither red nor black. They cannot be bet on at all.