wordpress will be prefectly fine. where you may have problems is in carelessly coded plugins - though that's not likely to be an issue either.
the rules do change a little between php4 and 5, but not so much that many people notice the difference at all. Generally speaking, there are enough people using either platform now, that any plugin authors tend to get feedback from their users and fix this stuff long before it becomes a problem for you.
I've upgraded very recently, and I had precisely one issue. A very minor one. I'll lay it out here just so that you know how trivial it was.
My issue was with my theme, which was my own doing. I had set my date format to (jS of F, Y) to read '7th of May, 2008' -- this works fine in php4, but in php5, the 'o' actually has a purpose, so my dates ended up being '7th 2008f May, 2008' -- that was easily fixed by escaping the extra crap in my date format like so: (jS \o\f F, Y) which if I were worth my weight in dog crap, I would have done from the very beginning.
That's it.. the sum total.
All in all, it's a good thing that your host is upgrading to php5, as php 4 is apparently no longer being supported by the php folks.