Trove

First of all, I suggest reading Jbeansem for the achievement below, which requires you to destroy 1,000,000 blocks which is a lot more.



Shortly into the game and completing the tutorial/quests in the top right, it will show you how to destroy blocks and build with them.

Press to enter build mode, and use to destroy the blocks. Keep it held down and simply destroy 5,000 blocks. It's a bit time consuming, it probably took me a couple hours but stick with it and you'll eventually have 5,000 blocks in your inventory.

I found it quicker to just look in 1 direction without looking elsewhere until you cannot dig no further. Then move over to either the left or right and do it again. The blocks seemed to be breaking faster whenever I was doing this and not looking all around breaking blocks another way.

Once you hit 5,000 blocks destroyed the achievement will unlock.