5. Solve the congruence $5 x \equiv 11(\bmod 43)$.
5. From $(5,43)=1$, using the extended Euclidean algorithm we have $5 \cdot(-17)+43 \cdot 2=1$, thus $x \equiv(-17) \cdot 11 \equiv-187 \equiv-15 \equiv 28(\bmod 43)$.