Sounds like the governor is sticking.
Check the linkage for any binding.

Sounds like the air filter may be dirty.

It depends upon what you consider "reving". If you mean that the engine speed pulsates from slightly above normal to slightly below normal, then I would think it's fuel related. Since it happened after 5 minutes, the first thing I would check is for a partially blocked vent on the gas cap, or a restriction in the fuel line.

If it's very high reving, as bill said.

Baymee, it is more like you described - the speed pulsates from higher than normal to lower than normal.

The springs are usually bent inward from hitting bushes and the rpm is slowed down. Sounds like a piece of dirt in the main jet. I'd remove it and clean it. Check for water in the bottom of the bowl.

Engine model and spec #s would be nice. Or even if it was a float type carb or a model w/ carb on tank.

"But, after about 5 minutes of cutting, the engine began alternating between reving and normal running"

"the speed pulsates from higher than normal to lower than normal."

What's next?

FYI it's a Sears Model 917.388190 with a B & S (550 Series) 5.5HP engine

That's a Briggs 10T802-1059-B1
It has the diaphragm type carb.

An accurate descriptions of the symptoms is important.
Whether it goes over speed leads down a different troubleshooting path, than if it does NOT exceed "normal" speed.

What I would first check is if the throttle plate shaft is binding at all.
I had an old tiller that had the throttle plate seize fully open (normal position with engine off) over the Winter.
Starting it in the Spring, the engine wanted to over rev to the point of destruction, since the throttle was wide open and the governor couldn't close it.
Yours may be binding "slightly". A bit of spray lube in the shaft bushings should fix that.

Another possibility is some water/bad fuel in the bottom of the tank.
The pickup for these carbs is right at the bottom. It maybe picking up some "bad fuel" intermittently. This would cause the engine to slow down. Bad fuel passes through and engine regains it's speed. This may "seem" like over revving when it really isn't.

Thanks for all of your replies!! But, here's my question now - Is this problem related to the NEW CARB that Sears just replaced?? I'm not great at knowing where all these parts are you guys mention like governor, throttle plate etc. Is this something Sears should be doing under my 90 day warranty for the new carb?? Or, should I just go ahead and fix it myself ?? Thanks again for your help. This forum is great for advice !!!!

It certainly is much easier to schedule an appointment with Sears than to go out and see if the throttle valve rotates freely.