Solution: 79,36 5. 

One way to tackle the problem is to find the first number consisting of all 1’s (called a repunit) that is divisible by 7. To do that, just set up a standard long division, adding as many 1’s as you need until you get a remainder of zero. You’ll get the equation 111,111 = 7 × 15,873, and because this equation is the smallest of its kind, we can multiply both sides by 5 to yield 555,555 = 7 × 79,365.

You can also multiply backwards to find the answer. That is, what number times 7 gives a 5 as the units digit in the result? Obviously, that’s 5. But then 5 × 7 = 35, so a 3 carries to the tens column. So then, what number times 7, and then adding the carried 3, gives 5? That’s 6, since 6 × 7 + 3 = 45. That gives a 4 that carries… and so on. This process will eventually lead to the answer, too.

Of course, the method that requires the least amount of thinking is to just use a calculator. Enter a string of 5’s, divide by 7, and keep increasing the number of 5’s until the answer is an integer.