I have tried to look powers of 5 in modulo 47 but It seems not working.
2026-04-24 15:52:57.1777045977
5 is primitive root on modulo 47 then solve the $x^{20} \equiv21(mod47)$
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As $5^3\equiv31\equiv-16,5^6\equiv(-16)^2\equiv21\pmod{47}$
Take discrete logarithm,
$20\cdot$ind$_5x\equiv$ind$_5{21}\pmod{46}\equiv6\equiv6-46$
ind$_5x\equiv-2\pmod{\dfrac{46}{(46,20)}}\implies x\equiv5^{23k-2}\pmod{47}$
Please use Solving a Linear Congruence to find $5^{-2}\pmod{47}$