It might be due to the fact that your InterNet Service Provider, who is providing your internet connection, may be blocking port 25.
This stops you from using any service other than their own to send email. This is becoming common with ISP’s as a security measure to reduce spamming.
To get rid of this you can try changing your email program to use port 26 for SMTP instead of port 25. Most of the servers has an alternate SMTP port as 26 inorder to fix ISP port 25 blocking issue.
How to add alternate SMTP port in EXIM.
Just add the below shown line in any part of the exim conf file.
♦ open the exim conf file (/etc/exim.conf)
♦ add the line
daemon_smtp_ports = 26