Sadly, I don’t think that approach is correct. The 5th percentile of a product of random variables is not the product of the 5th percentiles—in fact, in general, it’s going to be a product of much higher percentiles (20+).
As something of an aside, I think this general point was demonstrated and visualised well here.
As something of an aside, I think this general point was demonstrated and visualised well here.
Disclaimer: I work RP so may be biased.