=====Answer:=====

The shortest amount of time is 17 minutes.
For simplicity, we'll refer to each person by the time it takes to cross.
  - 1 and 2 cross
  - 1 comes back with the flashlight
  - 5 and 10 cross
  - 2 comes back with the light
  - 1 and 2 cross

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