If you want to move a bunch of keys without dragging them, select them all, taking note of the very first and very last keyframe numbers, and use scale keys - using 'new start/end times'. Now just punch in the new start and end times, of course adding the number of frames you want to offset by. So if your current start and end is 10 and 50 and you want to shift by 5 keys, you'd punch in...can you guess?... 15 and 55 for your new start and end times. Doing it from within the graph editor seems to be 'key' centric and from the edit menu it's somewhat 'node' centric, so pick whichever suits your need. Make sure the options are set properly.
Maybe I'm missing something, but I don't think I've ever used the dopesheet. I just don't see the advantage...I move keys in the graph editor the way you do in the dopesheet, with the move tool, using shift to constrain to time or values (horizontal or vertical). To each his own, I suppose, but I like to see my curves. I find the Graph editor easy as pie (and just as delicious). Then again I am sometimes forced use the Lightwave 6.5 'improved' motion curves (shudder - and it is actually much improved) or the absurd After Effects one (don't even get me started) so I LOVE the Maya graph. Maybe I'll mess with the dopesheet a bit.
"God saves those who save often..." - me.