It should work exactly like using Dropbox. Both Mesh and Dropbox use local folders that are monitored by a process and kept in sync that way. They both just look like regular filesystem folders to Calibre.
Also, unless your library mostly consists of picture-heavy books and technical manuals, 5GB is one massive library. If you're worried about the "what if?" scenario, measure your existing library and see where you're currently at. My library of some ~200 books is currently 375MB. I could fit 13 times the size of my current library in 5GB of space, so I figure it'll be quite a long time before I even come close to reaching the 5GB limit of Dropbox.