Highest Value Return

Hello all,

What function should I be looking to use if I want a formula to return the highest numerical value based off of the result of a If/Then statement?
Is there a function for that kind of thing?

Basically:

If(A5<>A4, [return highest numerical value in column AE], "")
I just don't know what function I'm looking for to complete the statement. Already tried CountIF and SumIF and those weren't quite right.

Evidently I didn't have this down quite as much as I thought.
Here's what I've got -
If('Wave 1'!E5<>'Wave 1'!E6), MAX('Wave 1'!AE:AE),"")

So basically, when E5 (and so on) and E6 (the cell below the first) are not the same, I need the highest number in Column AE up to that point. Then I need it to reset itself and start over from that line.

Does that make sense?

Evidently I didn't have this down quite as much as I thought.
Here's what I've got -
If('Wave 1'!E5<>'Wave 1'!E6), MAX('Wave 1'!AE:AE),"")

So basically, when E5 (and so on) and E6 (the cell below the first) are not the same, I need the highest number in Column AE up to that point. Then I need it to reset itself and start over from that line.

Does that make sense?