The easiest way to get all achievements (including this one), is to follow the following path;
First go for the following achievement:
Then start working on:
You have not enough slots for 5 tanks, so play each country one at a time. You will need to get to tier 3 for each country to be able to buy the 5 tanks you need.
While doing this you will most defiantly gain the following achievements:
In addition you most likely will win these:
You might also win, but from what I have noticed until now (I only did American tier and am now busy with UK, I had only 1 Tank Destroyer and that limits the play a bit):
That should get you on your way for the achievements :)