Evaluate $1234_5+2341_5$. Express your answer in base 5.
If the sum of any column exceeds 4, I need to carry over the excess to the next column, since 5 is the base. So, I write the numbers as follows: 1234_5 + 2341_5. Adding the rightmost column, I get 4+1=5. Since 5 is the base, I write 0 in the sum and carry over 1 to the next column. Adding the next column, I get 3+4+1=8. Since 8 is larger than 4, I write 3 in the sum and carry over 1 to the next column. Adding the next column, I get 2+3+1=6. Since 6 is larger than 4, I write 1 in the sum and carry over 1 to the next column. Adding the leftmost column, I get 1+2+1=4. Since 4 is not larger than 4, I write 4 in the sum and do not carry over anything. So, the final sum is 4130_5. 