Sure sounds like water damage to me especially since your noticing the rotten corner of the frame as well.
5 years is most definitely not the normal lifespan of an exterior door, but there are a couple of factors that may have added to the short lifespan, like lack of an exterior, good quality paint.
To repair the door usually takes longer and is less effective than a simple replacement.
To replace the door in most cases should be around 2 hours including removing and replace any trim.
Purchase a new exterior door (the right size
)
Remove the interior trim from around the door.
Remove the old door at the hinges. (makes the removal easier)
Looking between the door frame and the house studs you will probably see nails on either side (usually packed with shims) with a zawzaw cut these nails on either side and the door frame will slide out.
Clean out any debris from all sides of the opening. (rough opening)
Do NOT remove the new door from the new door frame, slide the entire replacement door into the opening. (remove the outer frame door lock retainer, leaving the male part still in the lock and jam, so the door doesn't swing open on you)
USE A LEVEL and make sure the new door is plumb and square to the opening, use shims to position the door correctly.
carefully remove the door retainer (in the lock key way) and while holding the frame open the door. On the hinges you will notice (usually) one screw missing, using the supplied screws with shims behind the the hinge, drive a screw in enough to hold the door. Check the plumb on the lock side and drive a screw in a third of the way down from the top. Back on the hinge side repeat the previous step (for hinges) on the bottom and then the same on the lock side.
You want three screws on each side, shims between the frame and studs at each of the screws, check for plumb and square then reattach the trim and lock set.
PS I always add "door and window" expanding foam (blue can)around all replacement doors.
do not use the max. expanding