After spending about an hour staring at these, I have found a recognition strategy that I think is fairly easy. So things that I noticed all these cases had in common was
1. They all have a 1x3 block.
2. If you line up the 1x3 block, then there is another solved edge that is not adjacent to the block.
3. They all have 3 unsolved edges when you line up the block.
4. There are 3 unsolved corners, but one of them is attached to an edge when you line up the block.
So I came up with a way to recognize the case by seeing what shape the 3 edges and the corner that is in a 1x2 block make.
F2 cases: If you look at the 3 edges, the corner that is part of the block, and the center, then it kind of looks like a paper airplane. So to recognize between the two F2 cases, see where the pointy side of the paper airplane is.
F3 cases: This one looks a bit like a cannon to me. To tell the difference see which side the cannon is facing.
F4 cases: From a certain angle this one looks like a dude with no arms and a long nose. See which way his nose is facing to tell the difference.
F5 cases: This is tricky because it also makes a paper airplane shape. But I noticed that unlike F2, the 1x2 is not adjacent to the 1x3. So that is how I would tell the difference.
Here are some visuals if you aren't seeing what I'm seeing.
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