Status update: I did move up to PHP 5.0 ans all is AoKay!
Note: I discovered that with my host GoDaddy I had to have "Hosting Configuration 2" (???) in order to run PHP 5.0. So, before I could up the PHP I had to let GoDaddy know to increase my "Hosting Configuration" to 2.0. Once that was accomplished I was able to go into my "control panel" and click on the PHP upgrade button.
There was no charge for either increase. Both changes required a few hours to "propagate" into/through the system. Also, neither change required any change to my website's name server addresses or anything like that.
I'm not all clear about the difference between "Hosting Configuration 2" and "1." It's all about GoDaddy rolling our more bells and whistles. But, it was something "good" and, like I said, there was no additional charge.