Similar question: https://gateoverflow.in/333214/gate2020-cs-17
So, the total number of relations over a set of $n$ elements is: $2^{n^{2}}$
No. of elements excluding the diagonal elements: $n^{2}-n$
These elements can either be chosen or not chosen. (we have to chose diagonal elements.So only 1 way to chose them all)
So, the total number of reflexive relations possible over a set of $n$ elements is: $2\times2\times....(n^{2}-n)times$ $=$ $2^{n^{2}-n}$
For this question, $n=5$ $\Rightarrow$ answer is : $2^{25-5}=2^{20}$
Option C is correct.