Vera has challenged Alexey to a round of Marker Mixup. Marker Mixup is a game where there is a bag of $5$ red markers numbered $1$ through $5$, and another bag with $5$ green markers numbered $6$ through $10$. Alexey will grab $1$ marker from each bag, and if the $2$ markers add up to more than $12$, he will win $\$5$. If the sum is exactly $12$, he will break even, and If the sum is less than $12$, he will lose $\$6$. **What is Alexey's expected value of playing Marker Mixup?** Round your answer to the nearest cent. $\$$ [[☃ input-number 1]]