Think of this "extra day" as an extra day to adjust and recover, not an extra day touring.
In my experience I write off the first day after traveling East as a complete loss. By the time I get home I'm so tired it goes beyond simple exhaustion. It's more akin to passing out due to alcohol or anaesthetic. I agree with the idea to get a nap in the hotel, though I would be more liberal with the length. Try to wake up before sunset and go outside while it's still light out. But don't be too surprised if you sleep for longer than you expect.
Traveling East is *definitely* harder than traveling West. And I actually find a 5-hour time difference just as hard as greater differences -- probably because of the inability to get a full night's sleep on the plane.