Quote Originally Posted by mc12345678 View Post
From where I *sit* the answer is yes you can upgrade the php version with no ill affect on a vanilla ZC version 1.5.5e. Throw in plugins, other software you might be running on your site, etc... and the answer becomes less so known. Ideally all of those/that are up-to-date for the span of versions supported by ZC (see the server requirements on the main page of this site: https://zen-cart.com).

As to being stuck with godaddy.... I can't disagree with frank on the recommendation to move away from them as a ZC host. It may not be what you want to hear, but think about the time and energy that could be saved by working on a platform that just works which in ecommerce turns into money made.
Yes, yes, and yes again - and no joke at all, but serious and genuine advice.