what is the purpose of number system conversions e.g decimal to base 5? I'm learning Number system conversion youtube. so far I know there are decimal, binary, octal, and Hex numbers. There is a purpose behind converting decimal to binary But what is the purpose of converting decimal to base 5 number?

Any choice of base is fairly arbitrary. Since we have 10 fingers on our hands, we use base 10. But we can use any other bases; lets explore some situations where they come up.
One example is that computers are very good at representing things in 2 positions. If we call one of those positions 0 and the other 1, we've suddenly imposed a base 2 system onto it, which we call binary.
Another example is that you can use your hands to count in base 6. On each hand, you can show a number of fingers between 0 and 5, so I can represent any number between 0 and 35 by multiplying the number of fingers shown on my left hand by 6, and adding the number of fingers on my right hand.
You could adapt the above system to base 5, for instance by ignoring your thumbs and instead multiplying the number of fingers on your left hand by 5 instead of 6. But this would limit the maximum number to 24, and it doesn't make as much sense.
So, what's the use of base 5? Knowing that its a tool in the toolbox, if a situation should arise where it's useful.
