If it were the battery, then chances are you wouldn't be *able* to crank it for 5 seconds. The starter should strongly turn the motor over for that length of time -- if it starts to slow significantly, then you may have a battery problem (now or more likely in the future). I'll assume that the battery is OK.
Quickly forget the injectors -- the newer designs and better fuel have pretty much erased that issue from this particular problem (15 years ago... sure). Actually, the only thing that affects driveability is the dispersion plate at the very tip of the injector -- sometimes, that can get partially blocked and cause a stumble on acceleration (for example), but generally not an extended crank issue. Today, the induction area is of more importance, particularly around the throttle body 'butterfly' valve. These often get choked with carbon deposits and cause idle concerns (i.e. hunting for idle), so it's a good idea to keep this area clean. Years ago, after cleaning them, we'd have to go through a 'learn' procedure for the engines' controller to adjust to the change, but most computers are adaptive enough not to need it these days.
Most times, this issue is the symptom of a problem in the fuel system. Jeep had a problem with earlier model GC's ('99-'01), and some '02's -- the fuel pump had an o-ring that cracked and allowed fuel to leak back through to the tank. Similarly, the pump has a one-way check valve that keeps system pressure as well. Unfortunately, this fuel is there as a residual to assist in starting the vehicle. You see, when the key is turned to the RUN position, the PCM will turn the fuel pump on for 3 seconds (PRIME), and that should be enough to pressurize the injector rail. Then, when the vehicle is cranking, it doesn't have to wait for fuel from the fuel tank -- its already got it. The first thing to do is put a fuel pressure gauge on the system, and see whether it has *correct* pressure at all the right times... 49.2psi +/- 5psi. For those earlier WJ's, there was a TSB that replaced that o-ring, and the later ones (like yours) required a replacement pump.