By definition of total relation, for every two elements $a,b$(same or different), $a\text{R}b$ Or $b\text{R}a$ Or both. So, every total relation is reflexive.
If $\text{A}$ relation $\text{S}$ is total and symmetric then relation $\text{S}= \text{A} \ast \text{A}$, i.e. $\text{S}$ is a universal relation on $\mathrm{A}$. $\mathrm{So}, \mathrm{S}$ is an equivalence relation.
The number of total relations on a set of $5$ elements is $3^{10}=59,049$.
Video Solution:
https://youtu.be/tqjuxfutFHg?t=142