Explanation:

Let’s break down the series step by step:

- The series is: 5, 8, 24, 57, 109, 184, 288, 423, ?

- Look at the differences:

8 - 5 = 3

24 - 8 = 16

57 - 24 = 33

109 - 57 = 52

184 - 109 = 75

288 - 184 = 104

423 - 288 = 135

- Find the pattern in differences:

3, 16, 33, 52, 75, 104, 135

- The differences between these numbers:

16 - 3 = 13

33 - 16 = 17

52 - 33 = 19

75 - 52 = 23

104 - 75 = 29

135 - 104 = 31

- Notice, difference of differences is gradually increasing.

- Add last difference (135) to last value (423): 423 + 135 = 558

- But check with next possible pattern (difference of 135, increase is mostly alternately by 4 or 6):

Recent increment: 13, 17, 19, 23, 29, 31

So, next likely increment: after 31 is likely 37 (as per twin prime step), so difference: 135 + 37 = 172

Adding: 423 + 172 = 595

Let’s Check The Options:

- 559

- 595

- 659

- 695

Option 2: 595 is the correct answer.