What number should replace the question mark (?)?

5, 12, 23, 50, 14, ?

The correct answer is 488.

Note on the Sequence:
The given sequence contains a typographical error in the fifth term. The number "14" is a print typo for "141". The correct mathematical sequence is:
5, 12, 23, 50, 141, ?

Let us analyze the relationship between successive terms by looking at their differences.

Step 1: Find the first-level differences
Calculate the difference between each consecutive pair of numbers:
$$12-5=7$$
$$23-12=11$$
$$50-23=27$$
$$141-50=91$$
So, the sequence of first-level differences is: 7, 11, 27, 91.

Step 2: Find the second-level differences (differences of differences)
Calculate the differences between the successive numbers in the first-level difference sequence:
$$11-7=4$$
$$27-11=16$$
$$91-27=64$$
The resulting second-level differences are: 4, 16, 64.

Step 3: Identify the pattern in the second-level differences
Notice that the numbers 4, 16, and 64 are consecutive powers of 4:
$$4^1=4$$
$$4^2=16$$
$$4^3=64$$

Step 4: Determine the next term
Following this geometric pattern, the next second-level difference must be:
$$4^4=256$$
To find the next first-level difference, add 256 to the previous difference (91):
$$91+256=347$$
Finally, add this difference to the fifth term (141) to get the missing term in the sequence:
$$141+347=488$$