Here's some performance info
Pulled this off an online Database.
I agree with the last post about not compromising field length, but I think that you should be fine based on the numbers I've seen. I;ve only flown the aircraft once, but am familiar with one particular operation and they routinely operate into a 3500 ft strip. Weather permitting of course.
PIAGGIO-DOUGLAS AVANTI P180
Engine: P&W PT6A-66 Wingspan: 46.00 ft
Horsepower: 850 Stall: 90 kts Length: 47.25 ft
Range: 1746 nm Height: 13.08 ft
Svr Ceiling: 41000 ft Empty Wt: 7200 lbs
Rate of Climb: 3000 ft/min Gross Wt: 10810 lbs
Max Fuel: 405 gal Single Eng ROC: 900 ft/min
Takeoff (over 50 ft obstacle): 2630 ft
Landing (over 50 ft obstacle): 2650 ft
Regards
Bman
PS
4000-5000 ft for a 5k turboprop is a bit of overkill don't ya think?