The short answer is the annualised volatility over twenty years should be pretty much the same as the annualised volatility over five years.
For independent, identically distributed returns the volatility scales proportionally.
So for any number of monthly returns
T, setting the annualization factor
m = 12 annualises the volatility. It should be the same for all time scales.
However, note the discussion here: https://quant.stackexchange.com/a/7496/7178
Scaling volatility [like this] only is mathematically correct when the
underlying price model is driven by Geometric Brownian motion which
implies that prices are log normally distributed and returns are
Particularly the comment: "its a well known fact that volatility is overestimated when scaled over long periods of time without a change of model to estimate such "long-term" volatility."
Now, a demonstration. I have modelled 12,000 monthly returns with mean = 3% and standard deviation = 2, so the annualised volatility should be
Sqrt(12) * 2 = 6.9282.
Calculating annualised volatility for return sequences of various lengths (3, 6, 12, 60 months etc.) reveals an inaccuracy for shorter sequences. The five-year sequence average got closest to the theoretically expected figure (6.9282), and, as the commenter noted "volatility is [slightly] overestimated when scaled over long periods of time".
over 20 years: 6.96
over 50 years: 6.97
over 100 years: 6.98
Annualised volatility for varying return sequence lengths
Edit re. comment
Reinvesting returns does not affect the volatility much. For instance, comparing some data I have handy, the Dow Jones Industrial Average Capital Returns (CR) versus Net Returns (NR). The return differences are somewhat smoothed, 0.1% each month, 0.25% every third month. More erratic dividend reinvestment would increase the volatility.