Answer
$\left\{1, 5\right\}$
Work Step by Step
RECALL:
(1) A is a subset of B ($A \subseteq B$) if all elements of A are also elements of B.
(2) A is a proper subset of B ($A \subset B$) if all elements of A are also in B but B has at least one element that is not in A.
The subsets of $\left\{1, 5\right\}$ are:
$\left\{\right\}
\\\left\{1\right\}
\\\left\{5\right\}
\\\left\{1, 5\right\}$
Notice that the first three subsets in the list are proper subsets.
The only subset that is not a proper subset of the given set is: $\left\{1, 5\right\}$
