bounds of beta distributions

I'd like to estimate the lower and upper bounds of a general beta distribution, using 5 and 95 percentiles. I already know how to estimate the mean and variance by the percentiles, such as Perry and Greig's approach.

Perry, C. and I. Greig (1975). “Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis.” Management Science 21: 1477-1480.