Given mask is $255.255.255.248$. That is, $255.255.255.11111000$.
Here, number of mask bits are $24 + 5 = 29$.
To find the number of subnet bits, look at the $last \space 8 \space bits$ of the subnet mask. The number of subnet bits are the number of $1$'s in the final byte. Here, we have $five$ $1$'s.
So, the answer is $(D)$.