Are you set on manufacturing these yourself? Because really, "best and most efficient" is to get a company with either large industrial machines or low cost labour to manufacturer this part for you.
If you're limited to a standard drill (hand drill, drill press, etc.) then you're going to get the most efficiency by stacking the parts so that you can drill multiple parts in one pass. The longer the drill bit and the larger the press, the more you can do at the same time.
Multiple spindle drills, as Daniel suggests, will give you another big bump in efficiency.
You can also scale up with people. A couple friends and a few cases of beer might go a long way.
You should also factor in that you will likely need to produce more than 5000 as your yield probably won't be 100% - some will get damaged, holes will be misaligned, etc.
Lets say you can drill 3 boards at a time with a standard drill (one hold), and 3 friends (4 people in total). You now need to each drill 1,250 holes. If you can drill 2 holes a minute (I'm just guessing here) you need 625 minutes or almost 10.5 hours each to complete this. That is only a day or two of work, just for the holes.