Normal rain has a pH of 6 while acid rain has pH of 5. Why is it so harmful in terms of acidity?

The pH scale is actually a logarithmic scale. What this means is pH is the negative of the logarithm of the concentration of hydrogen ions in a substance. Essentially, the more hydrogen ions there are, the smaller the number (and more acidic) a substance becomes. The formula is

pH = -log [H+]

So, to answer your question, while a range of 0 to 14 sounds small, the difference between a 5 and a 6 on the pH scale is by a factor of 10.

5 is stronger than a 6 by a factor of 10!