With going from 6 to 7 5 months may be tight but doable. We had gone from 6 to 7.1 with only myself doing the work and I started in February and we went live in May. My biggest recommendation is to have your business process buttoned up and know exactly what you do now and how you want to do it going forward. Some things can translate over and others don't very well. 7.5 is a leap forward from 7.1 and has some nice features that will save a little time such as built-in routing rules but you also need to know the limitations (those same routing rules don't allow you to route on everything in an incident as of the current release, but maybe soon).
I would say that the biggest gotchas for us were:
Emails and Email Templates
Routing Rules
Configuring Queues and permissions
Reporting
Training
The other item that takes a long time, depending on your business needs, is transferring closed tickets. It took us 3 days to transfer in 30,000 closed tickets from HD 6.5 and honestly we have NEVER looked at them. In fact I still haven't found a way to run a report against the migrated incidents at all.
All in all, if you keep it simple and don't have large demands for custom workflows up front, 5 months should work out ok.