Cutting 4 7/8" squares....
Like it said, cut the squares, draw the diagonal pencil line, then handpiece the scant 1/4 " up one side of the pencil line and back on the other side. Cut apart. Press. If your cutting and piecing were Very precise, when you press this it will lay on the table 4.5x4.5 inches which is the finished size. When you sew that HalfSquareTriangle into your block, it will finish to 4x4 inches.
To make it easier, personally and as Pam said above, if you started with 5 inch squares (I tend to start with 5 1/8" squares, hand piece either side of the pencil line, cut apart, press, then Square up to the unfinished size, which would be 4.5x4.5 inches. Starting with a little extra gives you some to trim off in the squaring up process and gives you perfect HSTs (HalfSquareTriangles)..