We're wary of upgrading the PHP version on our servers as it might break the existing scripts of some users. What we can do is migrate your account to one of our more recent Advanced Hosting servers. One that had a more recent version installed from the get go. Our Cherry server, for instance, uses PHP version 5.3.21, so that may be a good home for you. Migrations generally go smoothly. There may be some caching issues due to the IP change and if you use IMAP for email you'll need to update your IP or server address in your mail client settings.
If you'd like to proceed, please let us know by email.