The correct answer is $\boxed{\text{C}}$.

(Solution is omitted as per the original answer.)

Let the common difference of the sequence $\{a_n\}$ be $d$, and the first term be $a_1$. According to the problem, we have
$$\begin{cases} a_{1}+d=6 \\ a_{1}+4d=15 \end{cases}$$
Solving this system of equations, we get
$$\begin{cases} a_{1}=3 \\ d=3 \end{cases}$$
Therefore, $a_n=3n$,
Thus, $b_n=a_{2n}=6n$, and $b_1=6$, with a common difference of 6,
Therefore, the sum of the first 5 terms, $S_5=5\times6+ \frac{5\times4}{2}\times6=90$.
Hence, the correct answer is $\boxed{C}$.
By using the general formula of an arithmetic sequence and combining the given conditions to form a system of equations about $a_1$ and $d$, solving for $a_1$ and $d$ allows us to find $a_n$, and then we can use the formula for the sum of the first $n$ terms to solve the problem.
This problem tests the application of the general formula for an arithmetic sequence and the formula for the sum of the first $n$ terms. Proficient use of these formulas is key to solving the problem.