You can work this one out by making a grid with the A values across the top and the B values along the side. Each grid square represents a pairing like 1+2, 1+3, 1+4, 1+5, 2+2...Since there are four rows and four columns, there are 16 outcomes. The ones that don't exceed 5 are:
1+2=3
1+3=4
1+4=5
2+2=4
2+3=5
3+2=5
Therefore, the probability is 6/16 or 3/8