To estimate the average depth of rainfall over the basin within a 10% error, we need to determine the number of rain gauge stations required.

Let's assume that the actual average depth of rainfall over the basin is "D".

- The average depth of rainfall at the first rain gauge station is given as 105 cm.
- The average depth of rainfall at the second rain gauge station is given as 79 cm.
- The average depth of rainfall at the third rain gauge station is given as 70 cm.
- The average depth of rainfall at the fourth rain gauge station is given as 66 cm.

To estimate the average depth of rainfall over the basin, we can take the average of the depths recorded at the rain gauge stations. Therefore,

Average depth of rainfall over the basin = (105 + 79 + 70 + 66) / 4 = 320 / 4 = 80 cm

Now, let's calculate the maximum error allowable:

Maximum allowable error = 10% of the actual average depth of rainfall
= 10% of D
= 0.1D

To estimate the average depth of rainfall over the basin within a 10% error, the difference between the estimated average depth and the actual average depth should be less than or equal to the maximum allowable error.

Therefore, the condition for estimating the average depth of rainfall within a 10% error is:

|Estimated average - Actual average| ≤ Maximum allowable error

Let's substitute the values:

|80 - D| ≤ 0.1D

Simplifying the above inequality, we get:

-0.1D ≤ 80 - D ≤ 0.1D

0 ≤ 80 ≤ 0.9D

Dividing both sides of the inequality by 0.9, we have:

0/0.9 ≤ 80/0.9 ≤ D

0 ≤ 88.89 ≤ D

This means that the actual average depth of rainfall over the basin should lie between 0 and 88.89 cm.

To estimate the average depth of rainfall over the basin within a 10% error, we need to ensure that the estimated average depth is within this range.

Since the average depth of rainfall at the four existing rain gauge stations only covers the range of 66 cm to 105 cm, it does not cover the entire range of possible values for the actual average depth.

Therefore, additional rain gauge stations are required to estimate the average depth of rainfall over the basin within a 10% error. The correct answer is option 'B' - 5.