Because, though a4 does fight for control of b5, it doesn't do the same as e3, which is prepare for recapture and simultaneously prepare to fight in the center.
Queen's gambit declined Slav : why 5.a4?

Black's threat after 4... dxc4 (usually on move 4, not move 2, in the mainline Slav) is to play ...b5 and hold the pawn. After 5. e3 b5, white has a harder time regaining the pawn. 5. a4 controls the b5 square, so if black tries 5... b5, white regains the pawn immediately with 6. axb5 cxb5 7. Nxb5.

But still, why not just push a4 at a later point. I feel it would be stronger just to develop and gain a position edge for any pawns your opponent wastes time trying to hold on to.

timeless_thoughts' diagram is what I was referring to in my post. After 5. e3 b5, white has a harder time regaing the pawn (and developing effectively) than after 5. a4.

5 a4 is the main line in the 4...dxc4 slav but both 5 e4 and 5 e3 are playable and a lot of fun as well ! Kasparov himself has played 5 e4 !? before ( Geller gambit )
Hello everyone!
I was studying the queen's gambit the other day and I am wondering why the move 5. a4 is best in this opening : 1. d4 d5 2. c4 dxc4 3. Nf3 Nf6 4. Nc3 c6
Here's the position :
It is the usual continuation and my chess engine also says so. Why is it better than, say, 5. e3?
Thanks.