SMTP server: too many connections and service not available

Question

Hello my name is Prince...im trying to implement a register module to send a confirmation email to my client email address in asp.net. I'm using SMTP client to implement this. I used the following code:

    using (SmtpClient smtp = new SmtpClient())
            {
                using (MailMessage mm = new MailMessage("[email protected]", Email.Text.Trim()))
                {
                    mm.Subject = "Dummy";
                    mm.Body = "Body";
                    mm.IsBodyHtml = false;
                    smtp.Host = "smtp.gmail.com";
                    smtp.EnableSsl = true;
                    NetworkCredential credit = new NetworkCredential("[email protected]", "onukwilip2006+_");
                    smtp.UseDefaultCredentials = true;
                    smtp.Credentials = credit;
                     smtp.Port = 587;
                    smtp.Send(mm);
                }
            }
            

            ClientScript.RegisterStartupScript(this.GetType(), "alert", "alert(\"Mail sent successfully\");", true);

i used the above function in my button onclick, but when i send the smtp is telling me:

    Service not available, closing transmission channel. The server response was: Service not available

I've set my settings in account.google.com to allow less secure apps or something like that but the smtp is still not working.
It was telling me the below text the night before.

    Service not available, closing transmission channel. The server response was: Too many connections

But now its telling me the below code this night.

   Service not available, closing transmission channel. The server response was: Service not available

I also tried using the below function, but its still not working:

     using (MailMessage mm = new MailMessage("[email protected]", Email.Text.Trim()))
            {
                mm.Subject = "Dummy";
                mm.Body = "Body";
                mm.IsBodyHtml = false;
                SmtpClient smtp = new SmtpClient();
                smtp.Host = "smtp.gmail.com";
                smtp.EnableSsl = true;
                NetworkCredential credit = new NetworkCredential("[email protected]", "onukwilip2006+_");
                smtp.UseDefaultCredentials = true;
                smtp.Credentials = credit;
                smtp.Port = 587;
                smtp.Send(mm);
            }

            ClientScript.RegisterStartupScript(this.GetType(), "alert", "alert(\"Mail sent successfully\");", true);

Ive changed the port to : 25, 465,587 but still gives me the same error, when i set to 465 it tells me

    Failure to send mail

Ive checked google for some answers but none seems to accomplish or settle the problem. Please help me...

UPDATE: I just tried it again using smtp.gmail.com as the host and port 587. but its still telling me:

   Service not available, closing transmission channel. The server response was: Server busy, too many connections