Question : Problem: Error 550 5.7.1 in telnet

I have being trying to send an email to my gmail account using telnet but I received the following message:
550 5.7.1 Relaying denied

I am using as the smtp server address: smtp.google.com ; port: 25

Answer : Problem: Error 550 5.7.1 in telnet

This is because you are attempting to connect to the wrong host for sending mail via telnet on port 25.

In order to send mail to a gmail account like this, you need to connect to the SMTP server that is registered as their MX (Mail eXchanger) host.

Nslookup for gmail.com's MX record provides the following information for their MX hosts:
gmail-smtp-in.l.google.com.
alt1.gmail-smtp-in.l.google.com.
alt2.gmail-smtp-in.l.google.com.
gsmtp163.google.com.
gsmtp183.google.com.

Try telnetting to one of those hosts on port 25 and try your transaction again.