When you say it doesn't launch, does it do anything at all like throw up an error? Or show a splash screen and then quit out? A little more info would be useful to try and work through this, but there are some things you can try:
Hard reset your Xbox by closing all apps and games, then holding in the power button until the Xbox turns off. Unplug the power cable, wait 30 secs and then power everything back on again and try launching the game.
If that fails, try clearing the games saved data:
- Press the Xbox button on your controller to open the guide, and then select My games & apps.
- Highlight the Halo 5, and then press the Menu button on your controller.
- Select Manage game.
- Scroll to the right, highlight the saved data for your gamertag under Saved Data, and then press A on your controller.
- Select Delete from console to remove the local save of this game.
- Restart your Xbox and try launching the game.
If that also fails you could try reinstalling the game. You could maybe see if any other games or apps are unable to launch, I would probably reach out to Xbox Live Support for further help though.