I don't know how to do this without simple algebra which is not available to 4th graders, I think!
Allison must have 6 times the number of football cards altogether (5 sets of baseball cards each the size of her football cards collection plus the size of her football card collection).
Altogether she has 120 cards and this is 6 times the size of her football card collection; therefore, her football card collection must number 20 (6 * 20 =120).
Then she must have 5 times as many baseball cards, i.e. 5 * 20 = 100
Now baseball + football =100 + 20 as required.
I hope that is clear!