Isn't $5 trillion too much?
I tried searching for the USD money supply. According to this article on howstuffworks.com, the money supply (M0) in the US last year was $1.2 trillion.
I guess the money supply today won't be too different.
http://money.howstuffworks.com/how-much-money-is-in-the-world.htm
Do we need Bitcoin's market to be 4 times the US money supply before stability is attained?
I think you should compare bitcoin more to M2 than to M0. The reason is that bitcoin is already "bank accounts" and "saving accounts", and that there won't be fractional banking with bitcoin (there will always be a difference between 'true' bitcoins - those on the blockchain - and any stuff that looks like bitcoins but are just debt expressed in bitcoin. Only a fiat system, or a system where "real" money is stored and "certificates of money" are circulating allow for a confusion of both, and allow for fractional banking.
As you cannot loan out bitcoins, and keep them nevertheless simultaneously on your wallet, there can be no double-counting of coins (as it is with fiat money on bank accounts).
Which means that what we use as M2 money, will have to be supported by all of bitcoin if bitcoin is to replace fiat.
World-wide (all fiat money included, not just dollars), this is estimated to be equivalent to something like $ 55 trillion I thought.