In both 5.0 and 5.01: I'm hitting a hang.
'Twas a conventional start. No ships yet. I'm about 6 years in. I was doing 1-day increments; it dropped to a 40-second update, then 5 45-second updates, then it hung, so I assume it's something to do with NPR combat.
I've already sent the DB to your e-mail.
EDIT: Ok, I played through the hang. It looks like the precursors were fighting an NPR, and somehow the steps coming from 1-day updates were too big. This was probably to be expected, since the fact that the updates went from 1-day to 45 seconds is an indication that someone got into detection range much too quickly - it should have been something like 1-day to ~1-hour to ~1-minute. I ran up to the increment that hung without auto-moves on, then instead of giving 1-day updates, I gave it enough 5-second updates to get past the hang. I then gave it 2-minute updates for a while (until the missiles fired by the precursor had hit and the combat was over) then move up to 20-minutes, and now everything seems fine.
So I take two lessons from this:
1) Save often - fortunately I had just saved due to moving from 5.0 to 5.01 (just in case

). This let me easily replay the hang.
2) If you see the timesteps plummet and hit a hang, restore from a save, then run up to the point where they're about to plummet and play through with smaller timesteps.
John