You can use the internal login (keep it enabled) to let the 5,000 members use the slave site... but idk if they can use the master or other slaves. I believe (and I'm just starting to get used to it so can easily be wrong) that only members who are on the master site or register on a slave after being attached to the master can cross different sites.
Like I said,may be wrong... but I'd differently look into it or even open a support ticket before risking the 5,000 members.
It is supposed to work as you said, on different domains it only uses the same login information... but that was completely broke in 3.4.4 and even tho it stated to be fixed in 3.4.5, I can't get it to work at all. So be wary.