Question: What is the tens digit of the three-digit positive integer n?

Statement 1: The tens digit of (n+5) is 5.

by adding 5 in any number the ten's digit may change (if unit digit is greater than 4) or may remain same (if unit digit of number is less than 5) hence, the ten's digit of n may be 5 or 4 based on unit digit

since we have multiple values hence

NOT SUFFICIENT

Statement 2: The tens digit of n is less than the tens digit of 10n

i.e. ten's digit of n is less than the unit digit of n (because by multiplying 10 in the number, the unit digit of number shifts to the tens place of result)

NOT SUFFICIENT

Combining the two statements

ten's digit of n (which may be either 4 or 5) is less than unit's digit of n
i.e. unit digit of n is may vary from 5 to 9
in every case, adding 5 in n will change the ten's digit of number which becomes 5 after addition of 5 in n hence
ten's digit of n = 5-1 = 4

SUFFICIENT

Answer: Option C
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GMATinsight:
sir , quoting your line :
ten's digit of n (which may be either 4 or 5) is less than unit's digit of n
i.e. unit digit of n is may vary from 1 to 4
in every case, adding 5 in n will NOT change the ten's digit of number hence
ten's digit of n = 5

wont the value of n be in range from 145-149 ; tens digit would be 4..