AUTO DATE using IF condition

The only way that would work in Excel is if you had limited the number of iterations for calculations. Otherwise it would be a circular reference (a cell cannot reference itself or reference a cell that references itself). Limiting the iterations can have other effects (ie., incorrect results from not following the calculations to their conclusions). Regardless, Numbers does not have the choice to limit iterations so this formula will not work in Numbers. The only way to make an automatic timestamp is with a script running constantly in the background looking at the values in B5 and C5 (or values in all of column B and all of column C if you are doing the entire column) and placing/removing timestamps when it sees a change. It might mess you up, though, because it will steal focus to change the cell in column C, just as if you had gone to C to type in the time.