In some cases, ISPs block port 25 for their users. This will prevent your users from being able to send email from an email client through their ISP.
If this is the case, you can run exim on an alternate port. Port 26 is commonly used for this purpose.
Below are the exact steps do to so:
1. Log in to WHM. (http://serverip:2086)
2. Go to Service Manager.
3. Check the box for Exim on Another Port.
4. Set the port to 26
5. Click save.
Please note: If you are using a firewall, either hardware or software based, you will also want to make sure you have opened the port in the firewall.