Wonder Bread is just gross junk food. Also, if you consult the label again, it's worse than that. The 5g added sugar is for 57g of bread, so it's nearly 10% sugar by mass.
There are good brands here. I usually get Dave's Killer Bread. It still has some added sugar, but there are varieties with fairly small amounts.
They're still helpful in sorting out a 600 calorie meal that's going to keep someone on track to lose weight versus a 1200 calorie meal that is going to make them gain weight. Even if it's not exact, it's a useful guideline.