The 389CC OHV engine that's in your GP5500 is, itself, a Chinese Honda GX390 clone (sometimes referred to as a 188F based engine). This is the case for all Generac OHV engines, and the vast majority of generators on the market, even Briggs and Stratton's "powerbuilt" branded engines are GX390 knockoffs.

I service/repair/etc... GX and GX clone powered equipment (I'm factory authorized by 3 generator manufacturers to factory refurbish, and perform warranty repairs), and I've bought and installed hundreds of Chinese clone carbs over the years with a near flawless track record (less then 5% have issues of any kind). I actually set alerts for Amazon warehouse/open box deals on common carbs and snag good deals whenever possible. In this case you're looking for any GX390 generator style carb, here's one available open box for under $10

Ensure that your gaskets/mounting faces are in good condition/clean/not broken or worn anywhere, and if they are replace them (the carb linked above includes gaskets). Surging can sometimes be caused by a bad gasket allowing excess air into the carb.

Finally, as an addendum/because this was discussed elsewhere in this post if you're interested in converting to tri-fuel (Propane/LP, Natural Gas/NG, and Gasoline) there's complete carb and regulator combos also available. This one is open box like new for just $22, but it has a hose barb inlet connection that won't work with any quick connects BUT this $30 option has a threaded inlet with a barb that can be swapped out for a quick disconnect setup. I've previously purchased and installed both carbs, I prefer the threaded connections on the regulator but it's not difficult to make an adapter hose. Don't feel like you have to keep the regulator attached to the bottom of the carb either, I almost always extend the carb to regulator hose and mount the regulator to the frame. My personal generator setup is a 5500W Westinghouse dual fuel generator that I swapped the regulator it came with out for one of the tri-fuel regulators listed above (retained the OE carb/kept the carb that came with the kit as a spare), I use it with Natural gas as a backup at my home and propane when I'm running it to power my RV. I added a T fitting right off my gas meter, with a ball valve and 3/8 female quick connect fitting. I keep a 36' 3/8 rubber gas hose (with quick disconnects as well, of course) and 36' 30amp cable hanging on a hose reel mounted on the wall for easy hookups.

Only thing to keep in mind with propane and natural gas is they're lower power potential fuels, meaning my 5500W generator tops out at 4800W on propane and ~4500W on natural gas.

Any additional questions don't hesitate to ask!