Error code 5 means "access denied." Does The Forest have some kind of strict anti-cheat measures implemented? If so you could try enabling the anti-cheat compatibility checkbox in the game capture source.
Have you triple-checked that you aren't running any other software that includes any sort of overlay that can be displayed in your games? Examples include but are not limited to EVGA Precision, MSI Afterburner, Razer GameBooster, Razer Synapse, Dolby Axon, TS3 and Mumble Overlays, Fraps, Dxtory, the Curse Client, Raptr, Overwolf, etc. Some antivirus programs like AVG have also been known to break game capture, so be sure to whitelist the OBS directory. Some games also require that OBS is run as administrator, so right-clicking on the OBS shortcut and selecting "Run as administrator" can help correct the problem in some cases.