Gmail is taking exactly 5 minutes to show in inbox

I have implemented email service for my website in ASP .NET. This is my code

private async Task SendEmailInternalAsync(SendEmailDto sendEmailDto)
 {
            // create message
            var email = new MimeMessage();
            email.From.Add(MailboxAddress.Parse(sendEmailDto.From));
            email.To.Add(MailboxAddress.Parse(sendEmailDto.To));
            email.Subject = sendEmailDto.Subject;
            email.Body = new TextPart(TextFormat.Html) { Text = sendEmailDto.Html };

            try
            {
                
               var emailPrivateKey = Configuration.GetConnectionString("EmailPrivateKey");


                var credential = new ServiceAccountCredential(new ServiceAccountCredential
                .Initializer("x@y.iam.gserviceaccount.com")
                {
                    // Note: other scopes can be found here: https://developers.google.com/gmail/api/auth/scopes
                    Scopes = new[] { "https://mail.google.com/" },
                    User = sendEmailDto.From
                }.FromPrivateKey(emailPrivateKey));

                bool result = await credential.RequestAccessTokenAsync(CancellationToken.None);

                using (var client = new SmtpClient())
                {
                    client.Connect("smtp.gmail.com", 587, SecureSocketOptions.StartTls);

                    // use the access token
                    var oauth2 = new SaslMechanismOAuth2(sendEmailDto.From, credential.Token.AccessToken);
                    client.Authenticate(oauth2);

                    client.Send(email);

                    client.Disconnect(true);
                }

            }
            catch (Exception e)
            {
                _logger.LogError(e, "Failed during sending email.");
            }
        }

It is working just fine but causing a very weird problem. When I am sending the email outside my domain, It is taking exactly 5 minutes to show in the inbox. When I am sending the email to my domain emails, it is going instantly.

After few observation, The main thing I observed is the time which email is showing is exactly same time when I sent the mail but It is only showing in inbox after 5 minutes. Let me explain this with more clearly.

Let's say I am sending the mail at 2:48 pm. I receive the mail in my inbox at exactly 2:53pm but the interesting thing is gmail is showing the time 2:48pm only!!!