How to access smtp.gmail.com or other to send email

I followed your advice , I have an email account in smtp2go and this is my code but it do not works even not connects. I tested with cmd command from my pc with my smtp2go account and I had not a problem but with arduino does no connect.

thanks for your comments and sorry my english is not good.

#include <Dhcp.h>
#include <Dns.h>
#include <Ethernet.h>
#include <EthernetClient.h>
#include <EthernetServer.h>
#include <EthernetUdp.h>
#include <util.h>
#include <SPI.h>

byte mac[] = {0x90, 0xA2, 0xDA, 0x0D, 0x5C, 0x16};
IPAddress ip(192,168,1,5);
byte gateway  [] = {192,168,1,1};
byte subnet   [] = {255, 255, 255, 0};
byte smtp[] = {186,47,174,186};//{ 207,58,147,66 }; // I tried with two ip
EthernetServer server(80);                          //nslookup to smtpcorp.com

//IPAddress server(207,58,147,66); // conflicting declaration 'IPAddress server' -- and I do not why.
EthernetClient client;

void setup()
{
  Ethernet.begin(mac, ip,gateway,subnet);
  Serial.begin(9600);
  delay(1000);
  Serial.println("connecting...");
  if (client.connect(smtp,8025)) //2525/25/8025/587/465/8465 // I tried with all ports
  {
    delay(500);
    client.println("ehlo");
    delay(500);
    client.println("auth login");     
    delay(500);
    client.println(" name account base 64");  //mail account with smtp2go         
    delay(500);
    client.println("password base 64"); 
    delay(500);    
    client.println("mail from: mail account with gmail");  //This is related to smtp2go
    delay(500);
    client.println("rcpt to: xxxxxxxxxx");
    delay(500);
    client.println("data");
    delay(500);
    client.println("To: xxxxx");
    delay(500);
    client.println("From: xxxxx");
    delay(500);
    client.println("Subject: MENSAJE DE PRUEBA");
    delay(500);
    client.println();
    delay(500);
    client.println("ESTE ES UN MENSAJE DE PRUEBA DESDE ARDUINO");
    delay(500);
    client.println(".");
    delay(500);
    client.println("quit");
  } 
  else {
    Serial.println("connection failed");
  } 
}

void loop()
{
  if (client.available()) {
    char c = client.read();
    Serial.print(c);
  }
  while (Serial.available() > 0) {
    char inChar = Serial.read();
    if (client.connected()) {
      client.print(inChar); 
    }
  }
  if (!client.connected()) {
    Serial.println();
    Serial.println("disconnecting.");
    client.stop();
    while(true);
  }
}