We can solve this together! We're beginning with 345589 and removing 34057 from it.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 9 in column 1 and get 2.
2 is the first digit of our result.

Step 2: We'll start by subtracting the digit 5 and the borrow 0 from 8 in column 2 and get 3.
3 is the next digit of our result.

Step 3: We'll start by subtracting the digit 0 and the borrow 0 from 5 in column 3 and get 5.
5 is the next digit of our result.

Step 4: We'll start by subtracting the digit 4 and the borrow 0 from 5 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 4 in column 5 and get 1.
1 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 3 in column 6 and get 3.
3 is the next digit of our result.

So, 345589 - 34057 = 311532.