For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets.
\[
\{13,2,6,18,16\}
\]
The number of subsets is

Step 1 ：The given set is \(\{13,2,6,18,16\}\).

Step 2 ：The number of elements in the set is 5.

Step 3 ：The number of subsets of a set is given by the formula \(2^n\), where \(n\) is the number of elements in the set.

Step 4 ：Substituting \(n = 5\) into the formula, we get \(2^5\) which equals 32.

Step 5 ：So, the number of subsets for the given set is \(\boxed{32}\).

Step 6 ：A proper subset is a subset that is not equal to the original set. So, to calculate the number of proper subsets, we subtract 1 from the total number of subsets.

Step 7 ：Subtracting 1 from 32, we get 31.

Step 8 ：So, the number of proper subsets is \(\boxed{31}\).