Quicksync is active if you enable your iGPU on your i5 in the BIOS and then go to desktop>rightclick>screen resolution>detect display>find the grey one (check via advanced settings that this is your Intel HD GPU, not your dedicated GPU!), force it to use "display device on: VGA" and "extend desktop to this display", click apply and then try to set OBS to quicksync and just start a preview.
This should work if you have the driver installed.