It shouldn't. There's a huge amount of backward compatibility between PHP5 and PHP4. I can't make any guarantees, but PHP4 is not going under any further development, and PHP5 was released in 2004.. so it's pretty rock-solid at this point with many, many improvements.
There's been quite a few users that have gotten their hosts to switch for them, and it's usually a very quick and easy process. Many times, it can be done with the flick of a switch in the hosting's administration area.
The below may help get you started for GoDaddy:
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help.godaddy.com/topic/419/article/3937