Who knows about 5.5 hp governor Honda power??

I have serviced dozens, and dozens of those and hundreds if you include all the other governed small engines. I know I could fix yours, probably in seconds if it was in front of me, assuming the governor is still intact inside the engine, which since it's a honda, I do not doubt that it is.
I am not saying I can help you from this side of the keyboard, But I can try.
Ok so first things first ; Engine OFF, check the oil level !, lol.
Then; put all the springs back where you found them and show me the pictures, and I'll try to make sure you have them in the right places. I think they only fit one way.
next;
Close the throttle, and look down the carb, to be sure the throttle valve is Fully closed and that it is NOT loose on the throttle-shaft, and is not hanging up in the bore. If it is not, fully closed, I bet you tightened that little black plastic screw on the side, as far as it goes lol. So go back it off until ONLY 1/8th of an inch of plastic is visible, protruding out the back of the aluminum lug. This is your idle-speed screw. It serves double duty to hold the Idle jet in the passage. and If you were to take that Jet outta there, you would find two very tiny O-rings on the shaft of it, that seal the transfer passage to and from the low-speed circuit. But I'm not concerned about that so leave it alone for now. Now, With the idle speed screw backed off, the throttle-valve should be open just a bit. You will adjust this later.
Next,
move the throttle lever to WOT, and check that the throttle valve follows; AND that none of the moving parts rub on anything. This is very important.
Next, SLOWLY, move the throttle lever back and fourth checking that the throttle valve follows nicely, with no herky-jerky shenanigans.
Next
Now we can set the governor, but first I want to make sure it works.
There is a shaft coming up out of the crankcase and the governor lever is fixed to the top of it. Set the throttle lever closed towards idle. When the engine is running, the governor is ALWAYS trying to close the throttle valve, against spring pressure. So operate that governor lever thru it's travel and make sure it has at least some modest kind of operating range, and learn which direction it needs to move to close the throttle, and memorize that . Now go look to see if it is in fact, closing the throttle! If it is not, then you'll have to adjust something.
This is real simple; loosen the clamp, move the governor in the direction you previously memorized, and close the throttle valve, and hold them both closed, while tightening the clamp. When done, make sure the doggone clamp cannot slip, and again that nothing rubs on anything thing that it shouldn't.
Now you're almost ready to fire it up. Make sure the carb is secured to the intake. I leave the Air box off for this, but remove the little torque limiters out of the plastic business and put them on the studs, then the nuts, then snug it. I leave it off so I can keep an eye on everything, and if something ain't right, it's an easy fix.
Now, turn the fuel on, turn the choke on, and open the throttle lever about half way. and pull!
As soon as the engine starts
1) make sure the governor is working by reaching over to it and slamming the throttle valve closed against spring pressure, before the engine revs up to far. You know it should work, cuz we already pre-set it.
2) As soon as you have done that, open the choke and return the throttle lever towards idle.
3) now is the time to adjust that black plastic idle speed screw. Do not try to idle it too slow at first.
4) Tentatively work the Throttle lever, making sure the rpm goes up and down progressively.
5) when the engine has warmed up, from idle, whack the throttle lever to WOT and immediately close it. If the engine stalls or stumbles, it's probably because the idle speed is too slow.
If the engine accepts that abuse idle it down until it complains about it, then increase the speed screw another 1/2 turn minimum. Lets call this the sweetspot.
6) if the idle quality sucks, try adjusting the mixture screw . It has a very limited range, and is designed to augment the position of the throttle among the two or more low-speed discharge ports. so to get a good quality idle, once you have found "the sweet spot" as above, you may have to increase the throttle-valve idle opening, to get a good balance.
7) In my experience, every Honda small engine idles lean. So if you can't get it ticking over nicely and the gas is known to be fresh, and you KNOW the internal passages are all clean, Then you might have to modify the low-speed circuit.
BUT, ask yourself this, does this piece of equipment need to idle sweetly?
Usually the answer is no.
Ok so, that's about all I got.