13. Claudia has 12 coins in total, consisting of 5-cent and 10-cent coins. Using some or all of these coins, she can form exactly 17 different amounts. How many 10-cent coins does Claudia have?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
13. C.

Let Claudia have $x$ 5-cent coins and $12-x$ 10-cent coins. Then,
$$
5 x+10(12-x)=120-5 x=5(24-x) \text {. }
$$

Since these coins can exactly form 17 different values, therefore,
$$
24-x=17 \Rightarrow x=7 \text {. }
$$

Thus, the answer is $12-7=5$.