### Instruction: Convert $1357_{10}$ to base 5.### Response: To convert from base 10 to base 5, I need to repeatedly divide the number by 5 and keep track of the remainders.
The remainders will form the digits of the base 5 number, starting from the rightmost digit.
So, let me start by dividing 1357 by 5.
I can use long division or a calculator for this.
I get 271 as the quotient and 2 as the remainder.
This means that the rightmost digit of the base 5 number is 2.
Next, I divide 271 by 5.
I get 54 as the quotient and 1 as the remainder.
This means that the second rightmost digit of the base 5 number is 1.
I continue this process until the quotient is 0.
I divide 54 by 5 and get 10 as the quotient and 4 as the remainder.
The third rightmost digit is 4.
I divide 10 by 5 and get 2 as the quotient and 0 as the remainder.
The fourth rightmost digit is 0.
I divide 2 by 5 and get 0 as the quotient and 2 as the remainder.
The fifth and final digit is 2.
So, the base 5 number is 20412.