i am facing the problem in mail function in php.I have to pass more than 5 variables but its not taking that much

<?php
if (isset($_REQUEST['email']))  {

  //Email information
  $admin_email = "tripti.shaddhainfonewdelhi@gmail.com";
  $name = $_REQUEST['name'];
  $email = $_REQUEST['email'];
  $address = $_REQUEST['address'];
  $phone = $_REQUEST['phone'];
  $city = $_REQUEST['city'];
  $date = $_REQUEST['date'];

  //send email
  mail($admin_email, "$name", "$address", "$phone","From:" . $email);

  //Email response
  echo "Thank you for contacting us!";
  }

  //if "email" variable is not filled out, display the form
  else  {
?>
<?php
  }
?>