Just went through a similar dilemma myself in search of a 5-string.
I was really leaning toward wanting a 5-string Precision, but there is no MIM version (which would be in my price range). Alternatives from the Fender "family" would be the Fender 5-string MIM Jazz (passive), the Fender Deluxe Active J (which is ultimately what I chose), and the Squier Vintage Modified P.
You mentioned a Precision specifically, so short of an American version, that pretty much leaves you looking at the Squiers.
I wanted to love the Squier in the worst way. I kept a very open mind and while there are still lots of opinions, what I was hearing most from various forums and reviews was that their quality was significantly better than it used to be and these basses provided great value for not too much money.
From the photos I saw on line, I wasn't too impressed with the details - for example, no effort whatsoever to match the grains on the sunburst bodies. I played a couple locally and discovered several QC issues - pots that spun around in the body, bad setups, high frets, etc. The tech at one store spent about half an hour trying to get a Jazz version to a playable state and get rid of some awful fret rattle on the B and E strings to no avail, so I crossed the Squiers off my list.