The arithmetic mean of 100 observations is 50. If 5 is subtracted...

Let the original observations be $x_1, x_2, \dots, x_{100}$.

The original arithmetic mean is $\bar{x} = 50$.

The new observations are given by $y_i = \dfrac{x_i - 5}{20}$.

Using the property of arithmetic mean, if each observation is subjected to a linear transformation $y_i = a x_i + b$, the new mean is $\bar{y} = a \bar{x} + b$.

Therefore, the new mean is $\bar{y} = \dfrac{\bar{x} - 5}{20}$.

Substituting $\bar{x} = 50$, we get $\bar{y} = \dfrac{50 - 5}{20} = \dfrac{45}{20} = 2.25$.

Answer: $2.25$