Bxdty

From this video, I got know that Space Shuttle did reentry around 5000 miles away from landing site. It's angle of attack is maintained around 40 degrees during re-entry. If it is more than that, it bounces back to space.
Why don't we let the Shuttle bounce back into space many times as possible and skim a lot of atmosphere so that it loose lot of kinetic energy over there? I think bounce back causes intermittent heating so heat shield tiles get a lot of time of radiate heat out.

I think bounce back causes intermittent heating so heat shield tiles get a lot of time of radiate heat out.

Your thinking is reasonable as far as it goes...

But once you lose too much velocity and become deeply sub-orbital, you will sink like a rock into thicker atmosphere.

Within five minutes you'll either be toast from heating or jelly from pulling 15-20 gees.

In this answer I did a calculation for a different spacecraft (a Dragon capsule) with lift to drag between 0 and 0.3 and the scenario was always the same. Being significantly slower results in falling too deeply to quickly, and the higher density results in huge heat production and unsurvivably large accelerations.

Skipping reentries aren't unheard of. The Apollo command module performed a single skip when returning from lunar missions. However, there are several reasons why a skipping reentry (especially one involving multiple skips) would be disadvantageous for the shuttle:

1. As uhoh points out, a skipping reentry results in losing lateral speed at a very high altitude. In turn, you lose the ability to control your descent rate. By the end of entry you'd practically be in a free-fall which the vehicle would be unlikely to survive due to the heat and/or stress of attempting to pull out of the dive.


2. The shuttle's thermal protection system was not designed to withstand long drawn-out reentries. Here's a quote from the "Entry, TAEM, and Approach/Landing Guidance Workbook":
   
   

   
   

   On the flip side of high surface temperatures, there are high backface temperatures. If
   you fly at high temperatures for a long time, heat will flow through the tiles to the
   aluminum underneath. This can happen if you fly a low drag profile. In fact, backface
   temperature is the current low limit to the drag profile.

   
   

   
   


3. Several other systems weren't designed for long drawn-out reentries either. The APUs only have the fuel capacity to run for about 110 minutes, which wouldn't be enough to support both launch and an extended reentry. The radiators, which were cold-soaked before entry, may have needed additional capacity to absorb heat build up during entry. The RCS may have needed more reserves.


4. Flying a low-drag profile gives you less margin for error. Flying a middle-of-the-road drag profile means you have room to increase or decrease your drag as necessary in order to make the landing site. If your designed flight path is already on the low-end and you end up in a low energy condition, there's not much you can do about it.


5. It's not impossible to develop guidance for a skipping reentry, but it is definitely a more difficult problem.

I suspect there are other reasons I haven't thought of.

On the flip side, I can't think of any advantages. The shuttle's reentry was already comparatively gentle (well under 2g's the whole time) and the heat was perfectly managable as-is.