You can't actually merge contacts on the phone. It just links them together, but on the phone only (kinda like taking two contact cards and stapling them together rather than taking both cards and making one out of them). Most likely, the reason behind limiting it to 5 links is after that, with a lot of different contacts, it could start slowing things down.
The linking of contacts on the phone was designed as a way for you to link your Facebook, Twitter, Google+, etc contacts with your contacts from gmail (since gmail's contacts doesn't have a way to keep most of your external accounts tied with it), not for linking multiple gmail contacts together (since you should merge those).
If you go to http://contacts.google.com, under the More dropdown, select Find and Merge Duplicates. This will use Google's algorithms to try and best merge your duplicate contacts together. I found that the contacts it determines are duplicates are usually accurate.
If you find it didn't merge two contacts together that need it, you can click the checkboxes next to their name and then under the More dropdown, select Merge Contacts.
NOTE: Google+ contacts will automatically be linked through your gmail contacts.