The question may be ambiguous because the two numbers cannot be base 5 numbers since only the digits 0 to 4 are available. The numbers could be base 6 or higher, including decimal, so the first assumption is that the numbers are decimal but their sum is required in base 5. Decimal addition gives 133430 as the sum. To convert from decimal to base 5 we use the fact that 10 decimal is 20 in base 5; 100 is 400 in base 5; 1000 is 13000; 10000 is 310000; 100000 is 11200000. One way of converting decimal 133430 is by splitting it into 100000+30000+3000+400+30 and working out the base 5 equivalent for each multiple power of ten: 11200000+3*310000+3*13000+4*400+3*20. The multiplication must be in base 5: 3*31=143, 3*13=44, 4*4=31, 3*2=11, so we have 11200000+1430000+44000+3100+110=13232210, remembering addition must be in base 5.
Another way to convert to base 5 is to start from the left and multiply the first digit by 20 and add on the second digit: 23; then multiply this result by 20 and add the third digit: 1013 (using base 5 arithmetic) not 463, because 6 is 11 in base 5 and 4+1=10 in base 5; continue in the same way: 20310+4=20314; 411333; 13232210.
If we instead make a second assumption, that the numbers are written in base 6, then we must use base 6 addition: 122315+11115=133434. In base 6, 5+5=14 (6, carried over as 1 to the next place, plus 4).
