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 $x$?