In base 5 the place values (from right to left) are the ones place, the 5's place and the 25's place. The highest digit you can write in any column is a 4.
333 would be (3 x 25) + (3 x 5) + (3 x 1) which is 93 in base 10.
30 would be (3x5) + (0 x 1) which is 15 in base 10.
The sum of 93 and 15 is 108 in base 10.
Now lets write that in base 5 - We can have 4 25's so there will be a 4 in the 25's column. Since 4 x 25 = 100 we still have to account for 8 to get to 108.
We can have 1 five in the 5's columns since 1 x 5 is 5. Now we have 3 left over which we can place in the one's column
Final answer 333₅ + 30₅ = 413₅
