Verified answer

Since x ≡ 5 (mod 8), we can write x = 5 + 8n for some integer n.

Substitute this into the second congruence:

5 + 8n ≡ 7 (mod 11)

==> -3n ≡ 2 ≡ -9 (mod 11)

==> n ≡ 3 (mod 11).

Since n = 3 + 11m for some integer m, we have

x = 5 + 8(3 + 11m) = 29 + 88m.

Substitute this into the third congruence:

29 + 88m ≡ 1 (mod 3)

==> m ≡ 2 (mod 3).

Writing m = 2 + 3k for some integer k, we have

x = 29 + 88(2 + 3k) = 205 + 264k.

==> x ≡ 205 (mod 264).

I hope this helps!