A train leaves Thorn Junction at 1:25 P.M. and arrives in Niles at 3:05 P.M. The train makes two stops along the route for a total of 15 minutes.

The first train takes 1 hour and 40 minutes, plus 15 minutes for stops, for a total of 1 hour and 55 minutes of travel time. Therefore, it arrives at 3:05 P.M. + 1 hour and 55 minutes = 5:00 P.M.

The second train leaves at 4:30 P.M., so it will take (5:00 P.M. – 4:30 P.M.) = 30 minutes to travel from Thorn Junction to Niles. Therefore, the second train will arrive in Niles at 5:00 P.M. + 30 minutes = 5:30 P.M.

Answer: \boxed{5:30}.