The thousandth place in the number 5.135794695.135794695.13579469 is the third digit to the right of the decimal point, which is 555.
The digit immediately to the right of the thousandth place is 777.
Since the digit 777 is greater than or equal to 555, we round the thousandth place up by 111. Thus, 5.1355.1355.135 becomes 5.1365.1365.136.
5.136\boxed{5.136}5.136
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