On my Samsung S5 how do i get my emails to stay in my in box until i delete them
Make sure your Email account is set up as IMAP (not POP3). 

In theory POP3 downloads a single copy of the email to the device that requests it. In practive, i've noticed the same issue you described whereby Emails seem to disappear.

IMAP syncs a copy of the Email from the server to your device to ensure you can view the same mail on multiple devices.