We start by testing palindromic sequences in base 4. Since the positive integer must be greater than 5, we start by analyzing $22_4$, which is $1010_2$. We then test $33_4$, which is $1111_2$. Converting to base 10, we have $33_4 = 3(4) + 3 = \boxed{15}$.
Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.
{'answer': '15', 'subject': 'Number Theory', 'level': 5, 'unique_id': 'train/number_theory/193.json'}