iPhone - How to set up not requiring passcode if recently closed

I believe the setting you are looking for is Settings > Touch ID and Passcode > Require Passcode.

It should be noted that using a Microsoft Exchange account in email can effect the options available here. For example the only option on my phone is "immediately". this thread is how i finally learned why I only have the option "immediately".

You have to disable Touch ID for "iPhone Unlock" on newer iOS devices in order to set a time to lock your phone. In Settings > Touch ID & Passcode, disable (toggle off) Touch ID for iPhone Unlock. Once toggled off, you can then change the time to require passcode by accessing the "Require Passcode" option.

Basically it sets to "immediately" only with Touch ID enabled for unlocking your phone.