You Can't Probably Just Do Trial and Error 2.

$\begin{aligned} x \ mod \ 8 \equiv 2 \implies x = 8k+2 = 72q+34 \\ x \ mod \ 9 \equiv 7 \implies x & = 9a-2 = 72q+34 \\ & = 72(7+11w) + 34 \\ & = 538 + 792w \end{aligned}$

$8k+4 = 9a \implies k = 4 \ , \ a = 4 \\ \implies k = 4+9q \ , \ a = 4+8q$

x mod 11 = 10 => x = 11s-1 => 11s = 72q+35 => (11s mod 11) = (72q mod 11) + (35 mod 11) => 0 = -5q mod 11 + 2 mod 11 => 5q mod 11 = 2 mod 11 = (11c+2) mod 11 => 5q = 11c + 2 => c = 3, q = 7 => q = 7+11w , c = 3+5w

538 + 792w > 10,000 => 792w > 9462 => w > 11 => min(w) = 12 => min(5 digit number) = 538 + (792*12) = 10,042