Make it simple.
You have two dst-calculations. One with distance 7 miles and speed 160 mph that is not corrected for wind. One with distance 5 miles that is corrected for wind.
Solve them (time is equal in both of them), correct to get the speed of wind instead of the plane and voila.
I can write the entire solution if you want to, but I don't think you need it if you just approach it again knowing it's only two simple equations that need solving.