The latest HipChat macOS app uses port 443 (normal SSL port) for chat communications. You can download it by going to https://www.hipchat.com/downloads.
However, despite that, you should still be able to connect to services on port 5223. Your machine can make multiple outbound connections to servers on the same port (e.g. one to Apple's servers and one to HipChat's). If you're having issues connecting, it likely means there is a firewall preventing connections on 5223 or some other local network issue. You can see instructions for helping troubleshoot connection issues at https://confluence.atlassian.com/hipchatkb/unable-to-sign-in-to-the-hipchat-desktop-app-751436202.html.
If you continue to have problems, you can always drop us an email at support@hipchat.com and the team can help diagnose your specific situation.
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