### Instruction: Convert $1357_{10}$ to base 5.### Response: To convert a decimal number to another base, I need to repeatedly divide it by the base and write down the remainders in reverse order.
So I'll start by dividing 1357 by 5.
This gives me 271 as the quotient and 2 as the remainder.
So the last digit of the base 5 representation is 2.
Next, I'll divide 271 by 5.
This gives me 54 as the quotient and 1 as the remainder.
So the second to last digit of the base 5 representation is 1.
I'll continue this process until the quotient is zero.
Dividing 54 by 5 gives me 10 as the quotient and 4 as the remainder.
So the third to last digit of the base 5 representation is 4.
Dividing 10 by 5 gives me 2 as the quotient and 0 as the remainder.
So the fourth to last digit of the base 5 representation is 0.
Finally, dividing 2 by 5 gives me 0 as the quotient and 2 as the remainder.
So the fifth to last digit of the base 5 representation is 2.
Now I have all the digits of the base 5 representation.
To write them in order, I need to reverse the sequence of remainders I obtained.