Throwing it down at 5 m/s will do basically nothing. That will simply cause it to advance in its orbit a bit. To deorbit, you need to throw it backwards, not down. However in this case, since the feather has a such a low ballistic coefficient, it will promptly deorbit from ISS altitude on its own, without you having to do anything at all. Just wait a bit.
Given a 10 cm feather with a mass of 0.05 g, I looked at two cases intended to bound the possibilities. The first case is that the feather trims to a face-on attitude, with the lowest possible ballistic coefficient. It reenters from the ISS altitude in less than three hours. The maximum deceleration is about 10 G's at 100 km altitude. My heating estimate is highly suspect (I am applying a blunt body formula with a nose radius based on feather feature sizes), but my rough estimate is $30\,\mathrm{W/cm^2}$, which is rather a lot for organic material. The feather would not look like a feather anymore.
However it is not clear how it would maintain that attitude. More likely would be a trim with the heavier part of the root of the feather forward. For that I used about 1/40th of the previous $C_D A$, measured from a Vulture feather. (Albeit at completely the wrong Reynolds numbers, but hey, this is just for fun.) Then I get that it decays from the ISS orbit in less than four days, with a maximum deceleration of 8 G's at about 80 km altitude. The heating is much worse, at $200\,\mathrm{W/cm^2}$. That is a typical Mars entry heat rate. The feather would be gone.
If anything, I suspect that my choice of approach and parameters underestimates the heating. So my conclusion is that, alas, the feather will burn up. And I had such high hopes for the feather.