For a child or teenager whose feet are growing, it is advisable to purchase shoes which are bigger than the actual feet by one or more size.
For adults, the actual size of the shoes varies depending on the manufacturer. Two shoes may have the same number 5 but the actual dimension may differ for 2 manufacturers.
The best way to check if a shoe fits is to actually wear them and walk or run in them. If the shoes are too small, your feet will hurt. If they are too big, your feet will slip out of them when you walk.