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

5 2/7 = (7 5 + 2)/7 = 37/7
4 1/18 = (18 4 + 1)/18 = 73/18
5 1/24 = (24 * 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 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 8 + 3 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.