That's assuming you can have rank 5 Tumble at "lvl 5-6ish", which isn't possible.
Regardless, yes, a BF Sword first will do more damage then a Sheen can do, but that isn't the reason for getting Sheen.
Sheen first is a cheap damage boost to your tumble, which lets you jump forward, poke, then get back taking very little or no damage in return if done right.
Sheen first lets you quickly get to another important "Trinity Vayne" item: Phage. Phage gives some much needed survivability and the ability to start kiting effectively. It doesn't matter how sweet your BF Sword auto attacks are if you are getting hammered with damage in return. The slow on Phage, plus the health bonus might seem insignificant, but they are very helpful in the beginning phases of the game.
Sheen first lets you build into a faster Trinity Force. The move speed from Zeal, the burst proc of Sheen, and the survivability of Phage outweigh the benefit of overall increased damage from BF Sword. Then, when turned into Trinity Force, you get all those benefits, plus amazing damage.