How to move multiple frames at once?

Hi this is a very simple question that I can’t find a simple answer to.
I’m trying to move an animation of 15 frames to another part of my animation to align with a character on a layer beneath.

I use SHIFT+Select on all the frames to highlight them but by moving one none of the others move.

I don’t want to painstakingly move each frame to their right place ya know?

Sounds like you are doing it right?
Click the first cell, then hold shift and click the last (cells will be highlighted blue), release shift, then click and drag to new location.

More info from the Docs: Moving Cells

You can also select the cells as above, and cut and paste them using short cuts or using right click from the menu.