To solve this problem, we first need to convert all mixed numbers to improper fractions:

5 2/7 = $7<em>5+2$/7 = 37/7
4 1/18 = $18</em>4+1$/18 = 73/18
5 1/24 = $24\ast 5+1$/24 = 121/24

Now we can substitute in the values and simplify the equation:

37/7 + 3/8 - 51/56 - $121/24-73/18$ = 37/7 + 3/8 - 51/56 - $121/24-73/18$ = 37/7 + 3/8 - 51/56 - $121/24-73/18$ = 37/7 + 3/8 - 51/56 - $121/24-73/18$ = 37/7 + 3/8 - 51/56 - $121/24-(24<em>3+1)/18$ = 37/7 + 3/8 - 51/56 - $121/24-73/18$ = 37/7 + 3/8 - 51/56 - 121/24 + 109/18
= 37/7 + 3/8 - 51/56 - 121/24 + 109/18
= $37</em>8+3<em>7-51$ 8/7 56 - 121 7 3 3 18
= $296+21-51$ 8/7 - 121 * 7 + 3276

= $266$ * 8/7 - 847 + 3276
= 2108/7 - 847 + 3276
= 301.14

Therefore, the simplified answer is 301.14.