I would definitely go to a newer connector than 5.0.5, because I know there have been many bug fixes and improvements. Just go to
Zimbra Product Portal to see what's been added.
HOWEVER, not every point-release has been a 100% improvement across the board. So I can't guarantee that ZCO 6.0.2 won't introduce some bug that was not present in 5.0.5. But since you are upgrading, I would start with the latest ZCO for your ZCS and then see.
Also, I haven't personally upgraded to ZCS 6.x yet due to certain issues that apply to my site. I'm getting ready to upgrade to 6.0.5, or I may wait for 6.0.6, as those finally seem to deal with the concerns that I've had. I wonder why you upgraded to 6.0.2 when 6.0.5 is already out? If you're planning on upgrading again in the near future then, personally, I would wait until then to do a mass-upgrade of ZCO, unless someone has a specific problem that upgrading is likely to solve.