Versions 5 (late 1998) and 6 were fairly similar, the latter polishing on the previous. v5 was when the catalog spec was bumped up to 280 horsepowers. At a glance it seemed like the major improvements were strictly visual changes to body panels. What really happened inside was that the turbines were modified to ones that had some funky clay-like mold which got 'carved' to the right clearance with use.
Despite being more sophisticated and smooth, the newer turbines were said to be prone to problems at repetitive, higher loads. So some folks changed them back to those used in v4 due to its higher stability. Together with modified fuel management, it was able to bring about the above specs together with an improved steering shift and feel. Also worth noting was the aperture for squirting oil into the housing was made smaller but more precise. That helped in better lubrication at higher loads without risking the safety margins.
For v5, the suspension was refined into a fairly different taste. Originally, the top end versions had suspension that veered on 'nervous,' that was gradually toned down to reasonably sharp. This does not mean that handling was compromised in any way; it just meant that Mazda wanted people to be able to step on it more comfortably over a broader range of conditions. All models were designed to roll more in a natural way while still keeping the controllability beyond 'the edge.' People said it became less nervous and felt less anxious to 'step on it' in such tricky circumstances.
Around v3, all automatics were either 'Touring' X or S. Type X was replaced with the name Type RS. Type R remained as either type R or R Bathurst. The naming becomes really confusing. In v5, engines were separated into the 280 hps and 265 hps types. I think the only difference might have been the computer mapping. But cannot be sure. I haven't come across anyone who got the 265 hps version when 280 was available. Should one be tinkering with it anyway, the 265 version should not have been much different from the end results of tinkering with RS or R. Towards the end, the cheaper models were called RB.