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\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 566 with 5. Write the result 2830 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\phantom{\times999}2830\phantom{9}\\\end{array}
Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 566 with 5. Write the result 2830 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\phantom{\times999}2830\phantom{9}\\\phantom{\times99}2830\phantom{99}\\\end{array}
Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 566 with 5. Write the result 2830 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\phantom{\times999}2830\phantom{9}\\\phantom{\times99}2830\phantom{99}\\\phantom{\times9}5094\phantom{999}\\\end{array}
Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 566 with 9. Write the result 5094 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\phantom{\times999}2830\phantom{9}\\\phantom{\times99}2830\phantom{99}\\\phantom{\times9}5094\phantom{999}\\\underline{\phantom{\times}2830\phantom{9999}}\\\end{array}
Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 566 with 5. Write the result 2830 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}566\\\underline{\times\phantom{999}59555}\\\phantom{\times9999}2830\\\phantom{\times999}2830\phantom{9}\\\phantom{\times99}2830\phantom{99}\\\phantom{\times9}5094\phantom{999}\\\underline{\phantom{\times}2830\phantom{9999}}\\\phantom{\times}33708130\end{array}
Now add the intermediate results to get final answer.