My MySQL server is currently set to all default settings:

Key buffer size: Default
Maximum packet size: Default
Sort buffer size: Default
Network buffer size: Default
MyISAM sort buffer size: Default
Tables to cache: Default
Maximum number of connections: Default

The website has around 5,500 members online at once at it's daily peak, many of which using automated software for whatever reason, causing the database to give this error at random times:

"Can't connect to MySQL server on '0.0.0.0' (99)"
[Example IP]

I assume this is a problem with the handling of the cache and users so I was just wondering, based on the statistics, what the best settings for the MySQL database should be?
If it's some other problem I overlooked, then a resolution to that would be very appreciated too.

If memory serves error 99 means you have exhausted all your outgoing TCP ports. Meaning you have too many connections. What is your website coded in? PHP?

A couple solutions you can look at:
1) Use a persistent connection
2) Lower the connection timeout value

If memory serves error 99 means you have exhausted all your outgoing TCP ports. Meaning you have too many connections. What is your website coded in? PHP?

A couple solutions you can look at:
1) Use a persistent connection
2) Lower the connection timeout value

Yeah it's all done in PHP.
Thanks, I'll look into that.

Oh, forgot to mention, this error comes up every so often aswell:

Lost connection to MySQL server at 'reading initial communication packet', system error: 110