I know Microsoft likes pressuring you to upgrade your OS, but is it possible that Windows 7 users will get some love with Halo 5 at some point?
As an official release, absolutely not.
The whole purpose of giving Windows 10 upgrades for free was to get as much people as possible on a single version of Windows. That way they could drop support for Vista, 7, 8, and 8.1 and reallocate resources towards a single operating system, instead of wasting them on legacy tech.
Sorry OP, Halo 5 Forge uses APIs and features of Windows 10 that just aren’t available to earlier versions of Windows. It’s not possible for it to work on Windows 7 or 8.