Hi,
If your VPS has ConfigServer Firewall (CSF) installed then this would most likely be causing the problem.
You will need to review the firewall configuration on the VPS and ensure hose ports are allowed outbound.
You have to allow outgoing traffic to ports 25, 465, 587 and in the case of Mandrill 2525 as well.
You should actually be fine enabling only the one you will connect to. So:
sudo vim /etc/csf/csf.conf
add 25,2525,465,587 to TCP_OUT, and to TCP6_OUT if you use IPv6.
You might also need to remove that ports from SMTP_PORTS if you have SMTP_BLOCK enabled (if it is set to 1).
It’s better to contact your Web Host with the above response and I am sure that we will be able to help you out.
Thanks