The half life of a radioactive substance is 5 years. After $$x$$ years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of $$x$$ is ______.

We need to find the time for a radioactive substance to reduce to 6.25% of its initial value. We recall the radioactive decay formula $$N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}$$ where $$T_{1/2} = 5$$ years is the half-life. Setting up the equation, $$\frac{N}{N_0} = 6.25\% = \frac{6.25}{100} = \frac{1}{16}$$ gives $$\frac{1}{16} = \left(\frac{1}{2}\right)^{x/5}$$.

Noting that $$\left(\frac{1}{2}\right)^4 = \left(\frac{1}{2}\right)^{x/5}$$ and since $$\frac{1}{16} = \left(\frac{1}{2}\right)^4$$, we have $$\frac{x}{5} = 4$$ which yields $$x = 20 \text{ years}$$. The answer is 20.