Recipe says to bake chicken at 250 degrees for 5 hrs. how long does it need to be baked at 350 degrees?
Yes, you can.

In fact, one of the biggest, ever so often repeated mantras here is: 


  Don't determine doneness with a watch, use a thermometer!


Measure at the thickest part of the thigh, not touching the bone. If you have reached at least 165°F or  75°C, your chicken is done.

Of course, the hotter your oven, the crispier the skin will be and the higher the risk of burning some parts, so check your chicken periodically and tent with aluminum foil if necessary. That said, 350°F / 175°C is a perfectly reasonable temperature to roast a chicken.

I won't and can't give you a time to bake the chicken, partly because I don't know how large your bird is and what temperature it was at the start, because I don't know how reliable your oven thermostat is and above all: because only a thermometer can guarantee that the meat reached a safe temperature.