What do you mean "run a search"? You mean you want to get answers from 5000 people? No problem. The community version of Limesurvey does not impose any limits (which does not mean that there might be no limits by your server configuration, the database, etc.).
5000 respondents is not that extreme, so this should work fine if you have a fairly powerfull server / vps to run it on.
The most problematic part is probably concurrent responses (many people responding at the same time), which might overload your server. So ideally you send your invitations not all at once, but over the course of a few days to spread responses out over time and thus reduce the chance of high peaks of simultaneous responses.
I answer at the LimeSurvey forum in my spare time, I'm not a LimeSurvey GmbH employee.
No support via private message.
