Why is a SHA-1 Hash 40 characters long if it is only 160 bit?

One hex character can only represent 16 different values, i.e. 4 bits. (16 = 2⁴)

40 × 4 = 160.

And no, you need much more than 5 characters in base-36.

There are totally 2¹⁶⁰ different SHA-1 hashes.

2¹⁶⁰ = 16⁴⁰, so this is another reason why we need 40 hex digits.

But 2¹⁶⁰ = 36^{160 log₃₆2} = 36^30.9482…, so you still need 31 characters using base-36.