It seems strange that the 3rd gear synchro is bad... It is almost always the 2nd gear synchro that goes on the Mazda transmissions (the reason for this is the large split between 1st and 2nd).
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Originally Posted by josh18_2k
all transmissions grind going into reverse if you shift too quickly. clutch in, come to complete stop, wait a sec, then put it in reverse.
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Almost correct, the S5 transmissions had synchros in reverse. However, If that is the original transmission in that car, it would not have synchros.
The grinding occurs because the splines on the shift sleeve are moving at a different rotational speed to the splines on the inside of the gear when they are moved into contact with each other. Synchros avoid this by resisting shifter movement while applying force to draw the splines to the same speed. When the speeds match, the synchro quits resisting shifter movement and allows engagement of the splines.
It is possible to rev match and change gears smoothly without synchros, but it is much more difficult (especially downshifting).