1. The problem states John has 15 fast horses and 16 regular horses. 2. It also says 5 horses have both racing and regular genes, meaning these 5 horses are counted in both groups. 3. To find the total number of distinct horses, we add the two groups and subtract the overlap (the 5 horses counted twice). 4. So, total horses = 15 (fast) + 16 (regular) - 5 (both) = 26. 5. Therefore, John has 26 total horses.