Is this a private sale, or from a dealer?
See what records you can get. If you can get the VIN, have a Ford dealer run an OASIS report and see what work (if any) has been done at the dealer. See if the Check Engine light is on, or the "Green Wrench"
Just like an IDI, start it COLD..... if its warm, come back when it has sat and gotten cold. Turn on the ignition, and the WTS will light, on the 6.0's it is a squiggly line on the cluster, not a WAIT TO START light like you are used to...... it more than likely will have the later update in the PCM that will BUZZ the injectors while the WTS light is on. They do take a bit longer to start than the IDI's do. You will have to crank on it for 2-3 seconds before it will start. The HPOP (High Pressure Oil Pump) has to make 500PSI of oil pressure before the PCM will fire the injectors. When they catch they seem to all clatter to life at once...... Let it idle, the idle should be fairly smooth. Even being a newer diesel the 6.0 is still fairly noisy. It also has a much different sound than an IDI. It is a higher pitched knock that is not as hard of a knock as the IDI. You will also hear the injectors firing. This sound seems higher in the engine, and in some ways reminds me of noisy lifters in a gasser. If it has no tuner, there should be ABSOLUTELY NO SMOKE while it is idling. Depending on weather and mileage it may make a slight blueish puff right after it catches... (Mine has ~158,000 on it and when it is near freezing it will give a small puff on the initial cold start.). Now rev it a bit, it should rev smooth. If it has a miss while it is still cold, this is something called stiction. The shuttle valve in the injector will stick in the bore of the valve when the oil is cold and thick. Synthetic oil helps with this, which is why I run synthetic oil. Look at the oil filter (on top of the engine, center of engine, the larger canister, the smaller is the secondary fuel filter), the cap should not be very tall, and should have a 36mm hex molded into the top of it (the cap resembles the very end of a FL1995 filter). If the oil filter cap it tall, and kinda has the shape of a beer can, I would be leary. The aftermarket filters are not correct of the 6.0 and have caused damage in the past. As the engine comes to running temperature, the tone of the engine will change just a bit as the timing retards a bit.
Ask if any modifications/repairs have been done. EGR Delete, injector(s) replaced, any turbo work, head bolts/gaskets/studs? Has there ever been a programmer/tuner on it. Contrary to popular belief, it is possible that all this list is factory. If it had not had a tuner, and been well maintained, it could have all the factory parts, mine does.
Inside, look for normal wear. Remember, an 05 is 10 years old. Make sure the HVAC works if it is one of the automatic ones. The display in the overhead console may not work. This is a fairly easy fix, if it doesn't. If you find that issue, we can pursue that later. It will have 3 rows of seats. If the fronts are leather, all seats should be leather. May have rear heat and air and possibly a rear entertainment center. There are 2 seating arrangements, the more common, captain, bench, bench or the optional captain, captain, bench. It will have a "tri door" in the rear. A top liftgate and to lower barn doors. The barn doors are NOT metal, don't let that throw you. Also the 2 big windows at the rear sides are wing windows, the control is the 2 rockers in the overhead console.
Outside, look for the same. Also, take a good look at the passenger side. These things are BIG, and I have seen more than one Excursion with a bruise or three on the passenger side. (like the common caved in bedside in an Extended Cab truck)......
On your drive, play with it. A stock 6.0 has AMPLE power and is fun to drive. The button on the shifter is NOT an overdrive lockout like on the E4OD. It is a tow haul mode button. Turn it on, and you will understand why the manuals have faded away. It DRASTICALLY changes the personality of the transmission. If ESOF 4x4 make sure it works. If the HVAC defaults to the defroster for a moment when you shift, the seal in the knuckle is leaking (on my to-do list), but they are also a manual lock-out and can be locked, and when you change the switch, it just shifts the t-case. Also, if you are moving when you shift to 4x4, the PCM will "burp" the throttle during the shift.....
If you have any more specific questions, please feel free to ask. I've had my Excursion for over 8 years, and is currently my Daily Driver. There are some subtle cosmetic differences between my 03, and an 05.... but most of the truck is the same.