A permutation $a_1, a_2, \ldots, a_{13}$ of the numbers from $1$ to $13$ is given such that $a_i > 5$ for $i=1,2,3,4,5$. Determine the maximum possible value of 
\[ a_{a_1} + a_{a_2} + a_{a_3} + a_{a_4} + a_{a_5}. \]

Let's think step by step and output the final answer within \boxed{}.
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