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\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 52562 with 5. Write the result 262810 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\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 52562 with 5. Write the result 262810 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\phantom{9}\\\phantom{\times99}262810\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 52562 with 5. Write the result 262810 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\phantom{9}\\\phantom{\times99}262810\phantom{99}\\\phantom{\times9}105124\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 52562 with 2. Write the result 105124 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\phantom{9}\\\phantom{\times99}262810\phantom{99}\\\phantom{\times9}105124\phantom{999}\\\phantom{\times9}52562\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 52562 with 1. Write the result 52562 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\phantom{9}\\\phantom{\times99}262810\phantom{99}\\\phantom{\times9}105124\phantom{999}\\\phantom{\times9}52562\phantom{9999}\\\underline{\phantom{\times}262810\phantom{99999}}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 52562 with 5. Write the result 262810 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}52562\\\underline{\times\phantom{9999}512555}\\\phantom{\times9999}262810\\\phantom{\times999}262810\phantom{9}\\\phantom{\times99}262810\phantom{99}\\\phantom{\times9}105124\phantom{999}\\\phantom{\times9}52562\phantom{9999}\\\underline{\phantom{\times}262810\phantom{99999}}\\\phantom{\times}1171112134\end{array}
Now add the intermediate results to get final answer.