Not sure what you're asking here. Are you trying to sum 3 and 7 to a different base? In decimal the answer of course is 10.
10 means the base as a number to that base. If the base was 5, 10 would be the number 5 itself. If the base was 2, 10 would be the number 2.
In base 5 we would count 0 1 2 3 4 10 11 12 13 14 20, corresponding to the numbers 0 to 10 in decimal. In base 5 we only use digits 0 to 4; in binary (base 2) we only have digits 0 and 1.
In base 10 (decimal) we only have digits 0 to 9. In base 16 (hexadecimal) we have to invent symbols for digits we don't have: there's no single symbol after 9, so we use letters A to F to represent what we would write in decimal as 10 to 15. 10 in base 16 is the same as 16 in base 10.
What's 16 in base 5? Well it's 3 times the base plus 1: 31. What is 16 in binary (base 2)? 10 stands for 2; 100 stands for 4 (2 squared); 1000 stands for 8 (2 cubed); 10000 stands for 16 (2^4).
3+7=20 in base 5 and the sum totally in base 5 would be 3+12=20.