HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

When launching the game, it says that at least 5MB of free space is required on the disk and then it crashes. There is more than 20GB of free space on the disk. What is the problem?

This is an old bug that exists in all versions, and berserker tried to fix it, but it still remains.
The error is related to the fact that when the game was released, hard drives larger than 4GB did not exist.
To fix the bug, simply make a copy of a large file on the disk, for example, copy a movie or delete a movie. In general, you need to change the location on the disk where the game is installed.