Before your sixth time travel, you must pass Nex's test again. Don't get too comfortable, though. Nex will be much stronger this time around. Really!

When you defeat Nex, the Time Gate to the year 2503 will open.

You won't be authorized to travel though time unless you defeat Nex the Gatekeeper of Time.

Ah, you've passed Nex's sixth test. Now then, you should be able to access the Time Gate to the year 2503.

Take the Time Traveler's Pocket Watch and go through the Time Gate.

Come back after you've passed Nex's test. Nex the Gatekeeper of Time lives inside the Old Tree of Tera.