In a flower bed there are 23 rose plants in the first row, 21 in the second, 19 in the third and so on. There are 5 rose plants in the last row. Then the number of rows in the flower bed is:

The correct option is 10.

To find the number of rows in the flower bed, we can model the number of rose plants in each row as a sequence. Let us write down the number of rose plants in the rows starting from the first row:
First row = 23 plants
Second row = 21 plants
Third row = 19 plants
...
Last row = 5 plants

This sequence of numbers is:
23, 21, 19, ..., 5

Notice that the difference between any two consecutive terms in this sequence is constant. Specifically, the number of plants decreases by 2 in each subsequent row:
21 - 23 = -2
19 - 21 = -2

Since the common difference is constant, this sequence forms an Arithmetic Progression (AP).

For this Arithmetic Progression:
The first term, denoted as a, is:
$$a=23$$
The common difference, denoted as d, is:
$$d=-2$$
The last term (nth term), denoted as a_n, is:
$$a_n=5$$

We need to find the number of rows, which corresponds to the number of terms n in this progression. The formula for the nth term of an Arithmetic Progression is:
$$a_n=a+(n-1)d$$

Now, substitute the known values into the formula:
$$5=23+(n-1)(-2)$$

Subtract 23 from both sides of the equation:
$$5-23=(n-1)(-2)$$
$$-18=(n-1)(-2)$$

Divide both sides by -2:
$$\frac{-18}{-2}=n-1$$
$$9=n-1$$

Add 1 to both sides to solve for n:
$$n=9+1$$
$$n=10$$

Therefore, the number of rows in the flower bed is 10.