Hmm, 1724 will not do the job as it has absolute max vin at 6V.

What you need here is a Step-up/Step-Down converter at the sam time since input is within 4.4 to 6 volts while output at 5.

Maybe MAX856-859 is better for the case.

Can you afford to loose one battery cell? You will find more chips available.

Ioannis