The shortest amount of time is 17 minutes. For simplicity, we'll refer to each person by the time it takes to cross.

1. 1 and 2 cross
2. 1 comes back with the flashlight
3. 5 and 10 cross
4. 2 comes back with the light
5. 1 and 2 cross

1,2  -->   (2 minutes)
     <-- 1 (3 minutes)
5,10 -->   (13 minutes)
     <-- 2 (15 minutes)
1,2  -->   (17 minutes)