If you want to move your site from Joomla 1.5 to 3.x you have two possible ways to help you do the move.
You can sign up for a new hosting account which will put you on the latest PHP versions and in line for hosting Joomla 3.x. When you are happy with your new installation you can cancel your old hosting account and request that your domain name be pointed to your new account. Many users like to do this as it means that you can keep your old Joomla 1.5 website running while you get the new Joomla 3.x system up and tested,
2. Alternatively we will be happy to move your account up to a later server using PHP 5.4 +. This will bring you in line with Joomla's recommended configuration for Joomla 3.x. Please note that Joomla! 1.5 cannot work on PHP 5.4+ so any 1.5 installations will probably break when the account is upgraded.