Let,

The total number of people in the labor force of Pretendville in September = 1000x
No. of people in the labor force of Pretendville who were unemployed in September = 5.6% of 1000x = 56x
No. of people in the labor force of Pretendville who were unemployed in October = 5.9% of 1000x = 59x

how many people were employed in October of 2005 = 1000x - 59x = 941x

Statement (1) 10,000 more people were unemployed in October than in September.

This statement gives the difference in the number of people unemployed in September and October. By solving for x we can find the total number of people employed in October

This statement is sufficient.

Statement (2) In May of the same year, the number of unemployed people in the labor force was 135,000.

This statement gives information for the month of May which is not related to the question. This statement is not sufficient.

Answer is A

Another approach:

This is what the question stem tells us:
Let x be total population (remains constant)
# of people unemployed in September: 5.6%*x
# of people unemployed in October: 5.9%*x

We want to find # of people unemployed in October.

Statement 1)
Since there were 10,000 more people unemployed in October, we can use this information to equate the two equations we derived from the stem.
5.9%*x= 5.6%*x +10,000

Solve and find x (then multiply by 5.9%).
Therefore, sufficient.

Statement 2)
Irrelevant, so insufficient.

May be nitpicky, but the posed question never specifies the year in which the unemployment numbers were claimed, hence i chose E. Are we to assume that the question posed October & September data to be within the year 2005 even though it is not explicitly stated? Also makes me wonder why the question mentions a specific year instead of just the month. Looking for help - thanks