Answer
$1310_{five}$
Work Step by Step
Rightmost column:
$2+3=5=1\times5+0\times1=10_{five}$
record the 0, carry the 1
$. \quad 1$
$.\ $3 4 $2_{five}$
$+ $4 1 $3_{five}$
$\_\_ \_ \_ \_$
$\qquad 0_{five}$
Next column:
$1+4+1=6=1\times5+1\times1=11_{five}$
record the 1, carry the 1
$. \ 1\ 1$
$.\ $3 4 $2_{five}$
$+ $4 1 $3_{five}$
$\_\_ \_ \_ \_$
$\quad \ \ 1\ 0_{five}$
Next column:
$1+3+4=8=1\times5+3\times1=11_{five}$
record the 13
$. \ 1\ 1$
$.\ $3 4 $2_{five}$
$+ $4 1 $3_{five}$
$\_\_ \_ \_ \_$
$\ 1\ 3\ 1\ 0_{five}$
Test in base 10
$3\times 5^{2}+4\times 5+2=97_{ten}$
$4\times 5^{2}+1\times 5+3=108_{ten}$
$1\times 125+3\times 25+1\times 5+0=205_{ten}$
$97+108=105$
