Let's first use the given information to find the common difference of the arithmetic sequence.
The 2nd term is 26 and the 5th term is 47, so we can use the formula for the nth term of an arithmetic sequence to write two equations:
a + d = 26 (equation 1, where a is the first term and d is the common difference)
a + 4d = 47 (equation 2)
Subtracting equation 1 from equation 2, we get:
3d = 21
Dividing both sides by 3, we get:
d = 7
So the common difference is 7.
Now we can use the 2nd term and the common difference to find the first term:
a + d = 26
a + 7 = 26
a = 19
Therefore, the farmer had 19 cows in his first year on the farm. The answer is (D) 19.