Well, I've never tried my hand at racing, but at one time I rode my bike to work and back every day. (12 miles round trip is all it was) Ugh. I don't really know what a five degree slope looks like, but I know that there were a couple of hills on my route that were pretty steep. It took me a couple of months (this with doing some pretty intense PT every day, too) to get to the top without stopping or slowing significantly. Plus, I would practice riding around different areas on the island where there were LOTS of steep hills. Still took forever to figure it out. :)
The thought of climbing the Alps on a RACING bike (and not a mountain bike) makes me shudder! :)
Go Lance!
I tried "spinning" at the gym when that fad started. I hated it. I am not much of a bike rider either (I prefer to watch the peleton). Cycling and long distance running and swimming definitely require mental toughness and endurance, as well as physical.