Most webhosts will allow you to switch between PHP 5.2, 5.3 and now 5.4.
Although WordPress 3.5+ is PHP 5.3+ compatible, there might be some plugins or themes that use a few deprecated functions. Depending on your webhost's configuration, you may see these errors on your website, ie.: "X is using deprecated function Y".
The first thing to do in such case, is to ensure you are using the latest version of the plugins/themes, as they may have addressed those. But PHP can also be "silenced" for these particular errors, of which various methods are described here (related to WordPress):
In a worst case scenario, your webhost should allow you to switch you back to PHP 5.2 -- you can always ask their support staff if that's the case. But keep in mind that version 5.2 of PHP is no longer maintained by the developers of PHP.