I messed up - how do I recover deleted tracks.

I had a Sample Tank multitrack setup of 5 instruments on 5 tracks which I accidentally deleted all. I have saved the file since the deletion but not closed it. Short of going one undo at a time is there a way I can recover the deleted tracks?

You mean deleted in Reaper right? Not deleted from your hard drive (ie Drag to trash. Empty trash.) You could drag/drop the audio files back into the project. Use the 'Move items to source position' command if they don't start at zero on the timeline. Or... Do a 'save as' with a new name. Undo however many steps to get the files back. Save as with yet another unique name. Now open the previous save (with the deleted tracks but also new work) and copy/paste in any new work from after the delete into the new project. Do whichever one of those is quickest. :) However, if you meant you deleted them from your hard drive, then you would need to get into deleted file recovery. That means stop using that drive NOW before the data flagged as 'deleted, so OK to overwrite with anything new' doesn't get permanently lost and try something like Data Rescue.

Thanks for the quick advice. I decided to just sit and hit the undo key over and over and over [every volume tweeked and every knob I touched] until I saw the delete button hit on the tracks. All looks good now.

Sometimes that's easiest. :) You can have auto backups enabled and set it to save every 3 minutes (which I do). That's another way but you need to throw that switch ahead of time.