Using algebra-- "product of an integer and 5" means 5n, if n is the integer. The part where it says that the result is greater than -32, you put a " > (-32) " Putting this together, you get:
To find the least possible integer, divide both sides by 5:
5n/5 > -32/5
Since you need to find the least INTEGER, substitute an integer for n to find a close value.
-6 = -30/5 which is > -32/5 √
-5 = -25/5 which is > -32/5 BUT -6 is smaller
-7 = -35/5 which is < -32/5 X
So the integer that makes this true is -6. Check this by plugging it into the original equation:
5n > -32
5(-6) > -32
-30 > -32
To make sure that this is the closest solution, you can think that since each new value of 5n increases by multiple of 5 (5 is like the big multiplier here), you can't get any closer, without being smaller than -32.
Hope this helps, and please excuse my mathematical notation(s) !