@Cosmicwdwd There won't be a RPH.log if RPH is stuck at "Launching Game..." though. RPH will only start generating this log if it was able to launch without issues (so if it says "Enjoy..." and minimizes).
@MZabo I have a few more suggestions you can try:
Open the commandline.txt in your main GTA folder and replace all the text inside with the flag
-windowed
(that should be the only thing in the file). Save and close the file.
Ensure that neither the GTA5.exe nor the PlayGTAV.exe in your main GTA folder is set to "Run as administrator".
Go to the properties -> compatibility tab -> ensure the "run as administrator" option is not enabled.
In contrast to the previous point and to UnknownBastion's post, in my experience, it's better to run the RagePluginHook.exe as administrator (repeat the same steps as above but add the checkmark).
Although it's technically not about your error specifically, try following the instructions in the official RagePluginHook FAQ on pages 3-6:
add your GTA V folder as an exception to your antivirus settings
make sure no in-game overlays are active
set the permissions aka. security properties of some files and the GTA folder