Excellent point Nigel.

Okay, somebody check my math please.

According to the ideal gas law PV=nRT. Avogadro's n is a constant, and we can pretend that R and T are as well (to make it simple enough for me to handle). So, P (pressure) is proportional to 1/V (volume). Since density is mass/V, then P is directly proportional to density.

Now, air at sea level is 1/800 the density of water. And, pressure increases roughly one atmosphere for every 33 feet of depth.

So, air becomes as dense as water at a depth of 33x800=26400 feet.

Therefore, at five miles down, they ain't no hope of raising anything with bags or ping pong balls or anything else filled with air.

Is it possible to fill the bags or balls with a lighter-than-water incompressible fluid (e.g. gasoline or petrol)?

This is fun.