Numbers are placed in the figure below on the basis of some rules. Find the correct alternative to replace the question mark.

Let's analyze the relationships among the numbers row-wise or column-wise:
Method 1 (Row-wise difference pattern):

* First row: $5,9,14,20$

$$9-5=4$$

$$14-9=5$$

$$20-14=6$$

The differences between successive terms are consecutive integers ($4,5,6$).
* Second row: $9,17,27,?$

$$17-9=8$$

$$27-17=10$$

Following the pattern, the next difference should be $12$ (consecutive even integers $8,10,12$).

$$\text{Missing number}=27+12=39$$

Method 2 (Column-wise arithmetic pattern):

* Column 1: $5\times 2-1=9$
* Column 2: $9\times 2-1=17$
* Column 3: $14\times 2-1=27$
* Column 4: $20\times 2-1=39$

Both methods verify that the missing number is $39$.