You also need to think about if the ECU is different.
IIRC, some cars that are A/T in comparison to a M/T car is their ECU's are different. On another car I had, you need to swap over the ECU as well.
Your best bet is if you were wanting to swap your car to a 6-speed M/T, then your car should be manual already. When you involve electronics when doing a mechanical swap, you're only asking for trouble. Fortunately, a original 5-speed manual mazda5 doesn't have to deal with any electronics because a manual transmission doesn't really care in which gear it is, just as long as as you don't over rev.
I remember a long time ago, a friend swapped over a M/T to his A/T car, and found out there was no rev limiter because the ECU controls it. When the ECU doesn't have any feed back from the electronics of an A/T car, things get screwy. He had to find a M/T ECU for it to work properly.