Wow.. at least now I know why I don't trust any numerical info you gave
715.. nice I have one myself...(in much worse condition, nevermind the suzuki tank.. the only image I could find atm)

In fact I have the wheels it's sprocket and a new clutch within reach.
10.5" in diameter with chengshins 4.10's btw..
the original sprocket is #35 with 72 teeth.

your's will be different since your clutch is a #40 still;
as chancer said.. more like 60 teeth from the size of it.
the issue you're having more than just likely is the engine, not the gearing!
your carb needs to be cleaned, maybe the adjustement is a bit off;
or as OzFab suggested you only got used to the ~20mph the kart is capable of
and you need to remove the governor to increase the speed by increasing the rpms of the engine.
Now, I assume my butt's bigger than yours ...
since I have a second very similar kart

(just needed a manco drive wheel.... aaanyways),
it came with a 5hp flathead briggs,

and a 12T clutch and -buckle up- a 48T #35 sprocket

(tiny little thing.. cute almost) anyways it moved my butt up a rather steep hill
(the clutch is now toast though, hence the new one I got)
I
think the POs kid (half my weight perhaps ie. less than 100lbs)
wouldn't have killed that clutch in that setup..
I can't tell for sure of course.. all I can tell for sure, is that it worked for a very short time for me..
BUT keep in mind, that above is a 12T clutch on a 48T #35 (4:1)
your's would be slightly better 10T clutch on 48T #40 (4.8:1)
but let's be honest.. finding a sprocket that matches the Manco drive wheels six-hole pattern is not at all trivial.
much less finding one that is NOT of the manco recommended toothcount.
So yeah.. we're back at.. remove the governor if you want to increase speed, or buy a sprocket blank and have it machined to your bhc.
but first count the teeth of the sprocket you have thoroughly!
and do not reduce by more then ten percent at a time,
otherwise you might end up buying clutch after clutch since you burn them out like I burned mine.
'sid