Why would a calculator have base 5?

I have a calculator that I found recently that has a base 5 option. It has options labelled HEX, BIN, DEC, OCT, and PEN. My son set it on PEN, and no numbers above 4 worked anymore. Playing around with it, it was clearly base 5. (E.g. 22 divided by 3 is 4).

Why does any calculator have base 5? The other bases are commonly used in computer science, but I can't think of the slightest reason why anyone would need base 5 on a calculator.

The calculator is by Sharp, with the number EL-W535 and the word Writeview.

Solution 1:

Apparently, some computers in the 50's used a system to describe the decimal system which had base five digits, and another bit to represent if it was between $0-4$ or between $5-9$, known as a biquinary system.

Solution 2:

Base 10 is used because humans have 10 fingers. The base 5 could be the result of some inside joke or interest by a Sharp engineer. You can do base 5 arithmetic with one hand and count pretty high using two hands. Two-handed arithmetic in base 5 could be interesting, especially multiplication. But I can only guess.

Solution 3:

There are some cultures such as Gumatj that used base 5 with 25 the next level up.

Though I have to think that the real reason is the programmers for the calculator were playing an inside joke.