I believe the answer would be 20 because:
We have 5 routes that can be taken, we can label them as A B C D E,
Remember that the trip there and back have to be different (meaning no double combos)
The combinations for round trip (back and forth) are as followed:
AB AC AD AE
BA BC BD BE
CA CB CD CE
DA DB DC DE
EA EB EC ED = Total 20 Combinations.
I hope this helps!