Here's me reporting, 5 weeks later. The ball was on Saturday. Here are some observations that might be useful to share:
1) Five weeks are more than sufficient for you to gain a bluffer's knowledge of the Viennese waltz. Once deconstructed, the Viennese waltz is not that difficult. There are mainly three/four movements you need to master to hit the dance floor: right (natural) turn; left (reverse) turn; close change and/or hesitation (both to transit from right turn to left or vice versa). The actual moves are not difficult. What's challenging is to dance them to the fast beat of the Strauss waltzes.
2) What matters in the end is building muscle memory, especially with the footwork, which in turn calls for lots of practice. Which is what I did. I complemented my five hours of private lessons with "practice sessions" one hour a week where I went to dance the waltz in a group. I also literally waltzed everywhere to get my feet used to the moves so that they become second nature: I waltzed to the copier, to the bathroom, and when I think no one's looking, even to the Boardroom (the office was ideal because of the long hallways - I couldn't make two turns at home without hitting a wall). I waltzed on the sidewalk when no one's around, or on the platform while waiting for the metro. Crazy, but considering that I only had five weeks, I thought desperate measures were warranted. As the man, the biggest source of stress on the dance floor is to avoid the lady from colliding with other dancers. Thus if your feet can go on autopilot, you can concentrate on navigating.
3) While dancing with a partner that knows the moves as well as you do can be an amazing experience, I discovered that after five weeks, I was confident enough to lead even women who were less practiced than me but had some grasp of the rudimentary basics of the waltz. All it took was the confidence (and a bit of brawn) to sweep her off her feet and take her with you, and it worked out. (Well, in most cases, anyway).
4) I discovered that most women at the event could not dance. At least, they couldn't dance the Viennese waltz. So, while I was nowhere near being a good Viennese waltzer, five hours of private instruction turned out to be sufficient to impress many women on the dancefloor that night. (Either that, or they were all being kind and I was just lucky to end up with dance partners that knew how to accommodate my own flaws

)
In conclusion, yes, you can learn the Viennese waltz in five weeks. At least you can learn enough to get by and have a great time. I'm already looking forward to the next Viennese ball.