Fig. 5 extends figures 1 and 2 by performing a sensitivity analysis on the log-periodic formula with a second log-periodic harmonic (dashed lines in figures 1 and 2), in order to assess the reliability and range of uncertainty of the prediction. Using the fit shown in dashed solid lines in figure 2, we have generated 10 realizations of an artificial S&P500 by adding the GARCH noise (described in the previous caption of Fig. 4)) to the dashed solid line. We have then fitted each of these 10 synthetic noisy clones of the S&P500 by our log-periodic formula. This yields the 10 curves shown here in magenta. This test shows that the log-periodic formula with a second log-periodic harmonic (dashed lines in figures 1 and 2) is also providing stable scenarios: the precise timing of the highs and lows remain robust with respect to the realization of the noise. This conclusion is CORRECTING our previous incorrect conclusion of last month, based on a bug that we have now corrected. Last month, we were casting doubts on the robustness of the log-periodic formula with a second log-periodic harmonic (see Fig. 4 of last month which is INCORRECT DUE TO A BUG). This resulted from a bug in our program. The corrected program now confirms a robustness of the formula with respect to different noise realizations. The real S&P500 price trajectory is shown as the red wiggly line.