Now that V0.5.1 aka BotB day 5 februari update has been published here are some paths that I have been working on. All six paths include working in the store on day 2 and all but the first path include doing lifeguard duty on day 3. All six lead to Epiclust for 15 girls at the end of day 5. Each path is on a tab of the attached xls. Remarks per path:
1) the only one without the lifeguard duty. It is not really good, but I keep it in there to remember that doing lifeguard duty is the right decision for the current version of the game
2) contains the double at Bigdong and the highest score at 201 points. But not the best starting point for day 6 I think
3) goes for Viviane at Bigdong, but doesn't get much else. No second day in the shop, not gym membership etc.
4) a failed attempt to Epiclust 16 girls. The timing is there, all the girls are setup right to do it. But can't find the stamina needed to do it on day 5.
5) contains the second day in the shop and gets the gym membership. A total of 200 points and I think the best effort I have done yet. For this one see the result at the end of day 5 attached below.
6) An effort to get Chiyo into the mix. But the end result is disappointing at 187 points.
Note, you really need the februari update to duplicate these paths. I think none of them will work on the original public release of day 5 due to various bugs.