Mercury Sable when cold will crank but not start. When key is turned fuel pump makes noise approx. 1-5 minutes before shutting off. After it's shuts off car will start. shorter noise next start Why?

It sounds as if the fuel pump could be on it's way out, or/but more likely, you have 1 or more leaking injectors that are allowing the fuel pressure to drop down over time, and the longer between starts the lower the pressure gets which requires more time to get the system up to operating pressure. In either case though the 1 to 5 minutes on a first start sounds very excessive and you could have both a leak and a failing pump.

Thank you both for your help. Tom, it's the pump noise. When the car has been setting for a day or 2, the time is longer for the pump noise. My son said it was only about 2 minutes this morning, and then after that the car started right up with no noise. How extensive is it to test for leaks, replace injectors? approximate cost?