Eat more of the healthy foods you already eat, assuming you're already eating a healthy diet. If you need to, add a meal. Know that being thin is very healthy, and you're not underweight really. I'm the same height as you and until I got on antidepressants I weighed 155 and nobody ever accused me of being underweight. Now, if it's your looks you don't like, I'm assuming you want to put on muscle, which would require not only eating more but also starting a resistance exercise program.
Btw , Im a 23 year old male, 5'10 & in between 145-150 lbs , with a high metabolism