oh… I thought you were doing the work yourself.
If you have a stable website, running on a 5.x server I don’t think there is any reason to rush migrating to 7.
With that said, there are really two major extremes. One extreme is the transition is seamless (unlikely). The other is that the entire site blows up and costs to modify the existing script outweigh that of just completely redeveloping the site.
The first step though would be to audit of the website on 7 to figure out what breaks. Without any type of automated test cases the process is pretty much just manual QA of all the pages/features.