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 6 realizations of an artificial S&P500 by adding white noise to the dashed solid line. The white noise (shown as the blue dots) is drawn from a student distribution with 3 degrees of freedom and with a variance equal to that of the residuals of the fit of the real data by the dashed continuous curve. We have then fitted each of these 6 synthetic noisy clones of the S&P500 by our log-periodic formula. This yields the 6 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 providing quite unstable scenarios: the precise timing of the highs and lows seem to be quite sensitive to the realization of the noise. This suggests that the predictions based on the dashed lines shown in figures 1 and 2 are not reliable. The real S&P500 price trajectory is shown as the red wiggly line.