Android - How to get exact call time?

For Android 5.0.x Lollipop:

1. Either on "Recents" or "Call History", tap the entry you want to see. It will open a mini-menu under the entry with options "Call back" and "Details".
2. Select "Details" to see the call details.
3. From here, you can see the time when you receive/miss a call, and also the duration of the call.

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In addition to Andrew's answer, you need to click the entry and not the picture of the contact for the mini-menu to appear. I was clicking the picture of the contact, and it pulls up the contact info - not the call detail.