Answer
$4011_{seven}$
Work Step by Step
$(5\times 3)_{10}=(15)_{10}=2\times 7+1=(21)_{7}$
Record the $1$; carry the $2$.
$\begin{array}{llll}
& 5 & 4 & 3_{seven}\\
\times & & & 5_{seven}\\
-- & -- & -- & --\\
& & & 1_{seven}
\end{array}$
$(5\times 4+2)_{10}=(22)_{10}=3\times 7+1=(31)_{7}$
Record the $1$; carry the $3$.
$\begin{array}{llll}
& 5 & 4 & 3_{seven}\\
\times & & & 5_{seven}\\
-- & -- & -- & --\\
& & 1 & 1_{seven}
\end{array}$
$(5\times 5+3)_{10}=(28)_{10}=4\times 7+0=(40)_{7}$
Record the $40.$
Result: $4011_{seven}$
