Calculating The Difference Between Cells, But Using The Value Of Another Cell If The

I have the following on a spreadsheet that keeps track of when student work is handed in and calculates how many days late it is so a penalty mark can be given.

A1= User entered value : a fixed submission date that a piece of work is due to be handed in on.
A2 = User entered value : The date entered if work is handed in on time or early
A3 = User entered value : The date the work was handed in if late
A4 = User entered value : The date the piece of work is due to be handed in if an extension has been granted
A5 = Calculated value : How many days late a piece of work is

Essentially I want the calculation in A5 to reflect how many days late a piece of work is. SUM(A3-A1) would do this of course. If the work is early or on time, A2 is ignored.

Sometimes however students have permission to hand work in late, in which case another calculation is needed to work out how many (if any) days over their extension date (A4) their work is. How do I combine these two calculations into the same cell, so that if A3 is empty it checks A4 to see if the student has an extension date and then returns a 'days late' value if applicable?