Milly, inequalities can be confusing, but don't let them be!
If 4 boards cost $10, then one costs $2.50, right?
Let's let x = the cost of boards that he buys.
If he needs at least 5 boards, that would look like x > 5. Get it?
He's going to buy no more than 13 boards. x < 13.
We have to combine them, though. Remember that either can be reversed. Those would look like 13 > x and 5 < x.
If x falls between two numbers, we put it in the middle. The smaller number is 5, so it goes first, and the bigger number is 13, so it goes at the end.
So, that looks like 5 < x < 13. This is read as x is greater than or equal to 5 and less than or equal to 13.
Hope this helps!