using wait (bash posix) and fail if one process fails in a script

I am writing a script that executes a bunch of commands in the background all at once then waits for them to all finish:

#!/bin/sh -fx
./p1 &
./p2 &
./p3 &
./p4 &
./p5 &
wait

The problem is that if one or more of these processes fail, it just keeps going. How can I execute all of these commands at the same time and check if one or more fail?