and there are more than two clearly distinct ways to articulate a finger, so you can bump that up to at least 3^5, not that it would be in any way convenient or useful to do so
assuming you have the dexterity to hold each of your 10 fingers in one of 3 different positions—e.g.: up, down and crooked—you could technically count up to 3^10 or 59,049
if you mastered that, you could add a fourth or even fifth position. 4^10 is just over 10^6, so you could hold any 6 digits, and 5^10 is just under 10^7, so almost any 7 digits
you can compress really heavily using high bases, but for it to make practical sense the atomic medium of storage has to have that number of states
if you just convert binary to a high base and back again, unsurprisingly the space used works out exactly the same, as the number of symbols used to represent a number may be fewer, but the length of the symbols themselves balances it out exactly
e.g. in base 1000 you may be able to represent the number 999 with a single symbol, but you need 1000 unique symbols to show every number up to 999, each of which of course takes up significantly more digits than a bit; however, if you had a storage cell that could reliably store and display 1000 unique states, then it would be a different matter. whether that's possible or would/could even take up less physical space than ~log_2(1000) binary cells I do not know