### Instruction: Convert $1357_{10}$ to base 5.### Response: To convert a decimal number to base 5, I need to repeatedly divide it by 5 and record the remainders.
Then, the base 5 digits will be the remainders in reverse order.
So, let me start by dividing 1357 by 5.
I get 271 with a remainder of 2.
So, the least significant digit of the base 5 number is 2.
Next, I divide 271 by 5.
I get 54 with a remainder of 1.
So, the next digit of the base 5 number is 1.
I continue this process until I reach a quotient of 0.
Dividing 54 by 5, I get 10 with a remainder of 4.
Dividing 10 by 5, I get 2 with a remainder of 0.
Dividing 2 by 5, I get 0 with a remainder of 2.
So, the base 5 digits are 2, 0, 4, 1, 2, from right to left.
Therefore, the base 5 representation of 1357 is 20412.