Solve[x == a + (90 l + d1)/9 == b + (90 m + d2)/9 == c + (90 n + d3)/9 == d + (90 o + d4)/9 == e + (90*p + d5)/9, {l, m, n, o, p, x},
Modulus -> 90]
{{l -> C[1], m -> 1 + C[1] + 9 C[2], n -> 5 + C[1] + 9 C[3], o -> 2 + C[1] + 9 C[4], p -> 2 + C[1] + 9 C[5], x -> 16 + 10 C[1]}}
