How do I keep e-mail as new on iPhone 5?

If the email account is an Exchange or IMAP account and received email has been read with an email client on your computer or with another mobile device such as an iPad, all server stored mailboxes with an Exchange or IMAP account are kept synchronized with the server with each email client used to access the account including read and non-read status.

There is an option to mark read email as not read.

With the email selected and opened, select the Flag icon at the bottom left and select Mark as Unread.

And to do this for multiple emails, with the account's Inbox mailbox selected select the Edit button at the top right.

Select the emails you want to mark as read followed by selecting Mark at the bottom right and select Mark as Read.