I know that the distance that require the pilot to notify the control tower of an airport is 5 miles. Is the 5 mile distance the same for heliports, hospitals with pads, etc...?

In theory... true, but such heliports are often infrequently used an there may not be an authority to notify when flying in such airspace. Also, helicopters can reach 500'+ altitude with less lateral movement than a fixed wing aircraft so the 5 mile radius is overkill. If you know the authority to contact then you should do so but often these areas are just open fields or rooftops. Use your judgement.

Please see my post here:
http://forum.dji.com/forum.php?m ... D372%26typeid%3D372

You need to have a look at the aviation sectional chart that covers the area where you will be flying. If it is like the area within the faded magenta circle as shown in my example, you don't need to contact anyone regardless if a heliport is within 5 miles. This info is straight from the FAA; it is not just my opinion. An online sectional chart can be found here:
http://vfrmap.com
If you need help with that, tell us the location where you will be flying and I'll try to help.

As an over-simplification of what to look out for, if your flying area is within solid or dashed lines then it probably is in an area where you do need authorization. Tell us where you are. A street address will work.