Charles charges $4 per day to take care of his neighbors' dogs when they are gone. He also charges $10 to take out their trash once.

If the neighbors are gone for 5 days, how much money will Charles make?

If the neighbors are gone for 5 days, Charles will make 5 x $4 = $<<5*4=20>>20 for taking care of their dogs.

He will also make $10 for taking out their trash.
Therefore, Charles will make a total of $20 + $10 = $<<20+10=30>>30. Answer: \boxed{30}.