Official System Requirements - Heroes 5

Yes, of course, it will run; the requirements are 512 MB.
It might depend on the processor!!! :D :D :D

The processor isn't that important, although it is one of the main indicators.
The main things are RAM, the video card, and the processor.
I recommend 1 GB of RAM and a Radeon 9800 Pro or XT video card.
But that's to run the game at maximum settings! Otherwise, 512 MB will be enough!