The overall term \[Tr+1\] in the binomial extension is given by \[Tr+1\text{ }=\text{ }n\text{ }C\text{ }r\text{ }an-r\text{ }br\]

Here \[a\text{ }=\text{ }a,\text{ }b\text{ }=\text{ }-\text{ }2b\text{ }and\text{ }n\text{ }=12\]

Subbing the qualities, we get

\[Tr+1\text{ }=\text{ }12Cr\text{ }a12-r\text{ }\left( -\text{ }2b \right)r\ldots \text{ }\ldots \text{ }.\text{ }\left( I \right)\]

To disover \[a5\]

We compare \[a12-r\text{ }=a5\]

\[r\text{ }=\text{ }7\]

Putting \[r\text{ }=\text{ }7\text{ }in\text{ }\left( I \right)\]

\[T8\text{ }=\text{ }12C7\text{ }a5\text{ }\left( -\text{ }2b \right)7\]

\[=\text{ }-\text{ }101376\text{ }a5\text{ }b7\]

Consequently the coefficient of \[a5b7=\text{ }-\text{ }101376\]