The thousandth place in the number \(5.13579469\) is the third digit to the right of the decimal point, which is \(5\).
The digit immediately to the right of the thousandth place is \(7\).
Since the digit \(7\) is greater than or equal to \(5\), we round the thousandth place up by \(1\). Thus, \(5.135\) becomes \(5.136\).
\(\boxed{5.136}\)
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