Tire tread wear is not like an on/off switch, with things being totally safe one minute and totally unsafe the next. Instead, as the tread wears, you will be progressively subjected to more and more problems like hydroplaning while driving in the rain and less “grip” of the road on curves.
As was already stated, the economic difference between replacing your tires now, vs replacing them in 5k miles is negligible–unless you wind up in an accident because of the inferior traction of those badly-worn tires. In the event of an accident due to diminished traction, you will wish that you had not been such a penny-pincher.
Personally, I tend to replace my tires well before the wear bars appear on the tread.
I would much rather increase my margin of safety, as opposed to supposedly saving money by deferring tire purchase for a few months.