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?

Not much.  The only argument for base $10$ is that we are used to it, which is very strong.  Binary is useful for computer processing, but leads to very long expressions for numbers.  Years ago some computers would compress binary into octal, which cuts the number of digits by a factor $3$.  I worked on a CDC6400 that had $60$ bit words and the dumps were in octal.  I haven't heard of that for a long time, now it is all hex, which cuts the number of digits by a factor $4$, but I am out of touch and there could be some systems that still use octal.
Long ago I did a math puzzle that had $6$ everywhere in layers.  There was a bunch of computation to do, which I did in base $6$.  The puzzle could be solved without that.
I think there is value in recognizing the distinction between a number and its representation in some particular way. Expressed in binary, $\frac 15$ does not terminate, while it does in base $10$.  We get a number of questions involving terminating decimals that do not realize it depends on what base you are in.
