How many I have depends upon whether they are included in the tally or not.
The basses I use at the moment are 5 strings - my main one, another main one, a back up, an office one. So four.
I have two 4 string basses up for sale so they don't count. That leaves me with just one other 4 string I am keeping, but because I play 5 strings that doesn't count either, really.
Other, 'niche' basses that I have but don't use routinely - so don't count - are a Stag EUB, uke bass, fretless 5er, so that's three more not included in the reckoning.
But if you were being picky it could be ten. Which is actually less than it has been for many years - changing to 5 strings seems to have curbed my GAS to a degree. Although to be fair it is more about limited choices than any lack of desire on my part