I would suggest finding a different Mitel vendor, his answer is ridiculously absurd. If no other option is available, I would call and speak to his supervisor and explain the situation and request he come onsite and contact technical support to get it working. The setup itself is fairly simple, and spelled out pretty straight forwardly in the documentation. As long as IMAP is configured properly, the 5000 has the correct information in it for the IMAP server, and each user is properly configured with username, password, and server, it should just work. If this gets to be too difficult (I have had some situations where it just can't seem to be reliable), switch to the old method of non-enhanced integration (Basic copy or copy/forward) using SMTP, that is really simple.
As far as the LIM goes, I haven't used one in probably 5 years and that was on a 3300, so I can't be of much help there.