Because of this lore on the grumman gang is American General never tried to get the AA5 series certified for spins. The lore is that it can recover, but I'll let someone else try.
I realize that this is a rather old post, and, I ran into it why searching for information about the Grumman Cheetah.
I want to confirm that you can spin a Cheetah AA5A, even though it has a placard in it that says it's not certified for spins.
This event occurred decades ago when I first learned to fly. In fact, it was my very first flying lesson, and I didn't know the first thing about flying... nothing, really. We walk out to the airplane and I am taught how to do a preflight, we then climb into the Cheetah and my instructor gives me proper ground control procedures (my FBO was located at Houston Hobby - HOU - and I quickly learned big airport ops).
I get the right permissions, squawk the right codes and pretty soon we've taxied to 13L (now 12L) for a takeoff. I get the plane up to speed, pull back on the wheel and we are off! Of course, there's this high pitched buzzing sound but my instructor doesn't seem very concerned and we're headed for the skies. I was later to learn that the buzzer was the stall warning indicator and that I had a rather steep angle of attack. It was my first lesson in a Cheetah... you can take off pretty close to the edge without problems.
We head south of town and climb, and finally level out. No more buzzing... hey!... this is fun. After a while my instructor starts a conversation that goes like this.
Him: OK, I want you to pull back hard on the wheel.
Me: OK. (I pull back, the nose starts rising, the buzzer starts going off again). Hey, it's buzzing again.
Him: Don't worry. Just keep pulling back. (The nose keeps going up, the buzzer keeps going off, and the airplane is starting to shudder a little bit).
Me: It's beginning to act a little bit strange, real strange, actually. (Airplane really starting to shake and shudder... on the edge of a stall).
Him: Yeh, OK, we'll fix that. Push all the way down on your left rudder pedal. (Whoops! Wow! Zowie! What happened? It's a spin).
He then explains to me how to stop the rotation, then drop the nose and pull out of the spin. Pretty soon we're flying level again. He says, "Now, you never, ever want to do that by accident, OK? And, you never want to let this airplane rotate more than 3 times before you stop the spin, or you won't be stopping it.
We then spent the rest of my first training hour repeating the same stall, spin and recover routine until he thought I could perform the tasks properly.
That was my very first flight. Looking back, perhaps it wasn't such a good idea to spin the AA5A, but this instructor taught me so much about what the limits of an airplane are that I have always been thankful. If I had a question as to what the airplane would do, we'd go try it.