I'd wait until at least the s6 or s6 edge releases and go from there. Or if you want, you can wait until the lg g4 gets released and see of you want that more than what the s6/s6 edge has to offer.
Out of the current phones you listed, I have the s5 and I like it. It's very feature rich and the camera and battery are great for my needs. The turbo has a better battery and probably a smoother and less laggy interface, but it doesn't have te same feature set as the s5. The g3 has a better low light camera, but the s5 may have a better daylight camera. Both s5 and g3 have a good feature set, but if you want extra accessories and extra support, the s5 is better.