Hopefully someone see's this
PLEASE SOMEONE: THIS MAKES ABSOLUTELY NO SENSE WHATSOEVER
then why did you comment
For your sake I'll respond.
a4 is to prevent b5. Black can often play b5 after c6 to keep the extra pawn. If white plays e4 there black can play b5 and keep the pawn. a4 prevents that for now, and in some cases black can keep the pawn but usually not and black has to make huge positional concessions to do so.
To sum it up: To prepare e4 winning the pawn and controling the center without allowing b7-b5.
White is attempting to regain the pawn that he is down and simultaneously make Black pay for having violated opening principles by playing 4...dxc4. Capturing from the center out with a pawn is in most positions surrendering part or all of the center control that that center pawn controls.
With 5.a4 White is preparing to play e4 attacking the Black pawn on c4 with his B at f1. If Black plays 5...b5 then 6.axb5 cxb5 7.Nxb5 White has regained his pawn and Black has a weak isolated pawn at c4.
If Black plays 5...a6 then 6.e4 b5 7.axb5 cxb5 8.Nxb5 If 8...axb5 9.Rxa8 and White has won the exchange of White N for Black R.
I believe the above is sufficient to guide you.
The OP asked for an explanation of the move 5.a4. Not, what Black's next move should be. After 5...Bf5 White would play 6.Ne5 simultaneously attacking the pawn on c4 and preparing to make e4 possible.
I wrote that sufficient guidance was the goal of my explanation of the move 5.a4. Attempting to explain the theory of the Slav and any transpositions to other openings or variations is not answering the OP's question.
