elementary number theory - Find the last digit of the exponent $x$.

Let
\begin{align}
p&=396543857870745963499374527519378569849832249490600276007703072957912\cdots\\
&\phantom{=}8049490077183813353745228056691
\end{align}

This number is a 100-digit prime number and 2 is a primitive root modulo $p$. Let $x$ be the unique positive integer with $1 \leq x \leq p-1$ so that $2^x \equiv 5 \pmod{p}. $

What is the last digit of $x$?