Going on vacation to India for 5 weeks after applying for N400

You can travel normally. The only thing to keep in mind is that you will first receive a fingerprint notice (but you have a lot of time to get your fingerprinting done), and then an interview notice. If you travel when you might expect an interview notice, you would be well advised to have someone check your post occasionally to let you know when your date will be so you can make it back for that, or reschedule if necessary.
 
Top