My question is I have a ls hydro tranny and a quaife ls/b16 LSD and a set of gsr gears if I put 1-4th gsr gears into the ls and keep the ls 5th gear would the tranny work fine as far as shifting and using it to drag race?

 

If you build it correctly and have the correct parts to make the GSR gears compatible in the LS trans, it should be fine. Granted that all the parts you have are in good working order.