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ANSWER: 3 cows, 2 pigs and 1 horse.

EXPLANATION: You can use algebra to solve the problem:
1) Pigs + Horses = 3
2) Cows + Horses = 4
3) Cows + Pigs = 5

Use the first two equations and isolate for Horses:
Horses = 3 - Pigs
Horses = 4 - Cows
therefore 3 - Pigs= 4 - Cows

Replace Cows in the above equation with 5 - Pigs (from equation 3):
3 - Pigs = 4 - (5 - Pigs)
3 - Pigs = 4 - 5 + Pigs
3 - Pigs = -1 + Pigs
4 = 2 × Pigs
Pigs = 2

Replacing Pigs with 2 in equations 1 and 3 will give you the number of Horses and Cows.

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