How can I ripple delete frames in a timeline?

I have shortened my overall animation and now want to remove about 10 frames in the timeline and have everything after these frames move down the timeline by those 10 frames. How can I do this?

There's not a tool to specifically do this; you'll need to manually select keyframes and move them. The easiest method is to select all affected elements, and in the keyframe area drag-select everything after the time. Then hit the left arrow 10 times.