To add numbers in different bases, you should first convert them to a common base and then perform the addition. In this case, let’s convert both numbers to base 10 and then add them:

1. Convert 321 base 5 to base 10:
   • (3 * 5^2) + (2 * 5^1) + (1 * 5^0) = (3 * 25) + (2 * 5) + 1 = 75 + 10 + 1 = 86 base 10
2. Convert 413 base 8 to base 10:
   • (4 * 8^2) + (1 * 8^1) + (3 * 8^0) = (4 * 64) + (1 * 8) + 3 = 256 + 8 + 3 = 267 base 10

Now, you can add these two numbers in base 10: 86 + 267 = 353 base 10
So, the result of adding 321 base 5 and 413 base 8 is 353 in base 10.