To find the number of digits of a large number $N$, we calculate its common logarithm (base 10). The number of digits is given by $\lfloor \log_{10} N \rfloor + 1$ (the characteristic plus 1).

Let $N = 5^{20}$. Taking the base-10 logarithm: $\log_{10} N = \log_{10} (5^{20}) = 20 \log_{10} 5$.

We rewrite $\log_{10} 5$ using the identity $5 = \frac{10}{2}$: $\log_{10} 5 = \log_{10}\left(\frac{10}{2}\right) = \log_{10} 10 - \log_{10} 2 = 1 - 0.3010 = 0.6990$.

Now, substitute this back: $\log_{10} N = 20 \times 0.6990 = 13.98$.

The characteristic of this value is $13$. Thus, the number of digits is $13 + 1 = 14$.