I Am 5 Feet Tall And 10 Stone. What Would Be The Smallest Horse I Should Ride?

SIZE
The horse is capable of carrying a tremendous amount of weight.
The only time the relative size of the rider and the horse is
important is when showing, then the suitability of horse to rider
becomes an issue. Small children are better off on quite mispositioned
large horses than on small ponies that are wild.  Likewise, a small,
quite pony may be ideal for some; however the child will likely
outgrow this mount. A rider's leg ought to fit down the sides of the
horse's side in order to give leg cues (signals to the horse), but not
be so long that the leg from the knee down does not touch the ribs.
Most adults would do well to ride horses (over 58 inches at the top of
the withers). As long as the mount is quiet enough for the child to
work around and mount, the size of the animal should be considered
secondary.
OTHER INFO

Basically, the younger the rider the older the horse needed.
This is a function of training, calmness, and experience that comes
with an older horse rather than with age itself. For a novice rider,
it would be rare to find a horse under five that is trained and quite
enough

SOURCE: Purdue.edu AS-465 (Great source has everything from what to look for and how to start riding.)

Best of Luck to you horseback riding is alot of fun and owning your own horse makes it better.

5 feet is an ideal height to become a very good jockey. But you are over weight. Your weight should be 105-110 lb. If you don't want to be jockey then with your height of 5 feet you can ride any horse.