Step-by-step Solution:

In total, there are 5 horses. Out of these, Mr. A selects two horses. This can be done in \( \binom{5}{2} = 10 \) ways.
Out of the five horses, only one horse wins.
Let us say Mr. A has selected the winning horse. He has to select one more horse so that his set of two has the winning horse.
Out of the remaining 4, one can be selected in \(\binom{4}{1} = 4\) ways.
Thus,
The probability that Mr. A selected the winning horse is \( \frac{4}{10} = \frac{2}{5}.\)