Yes and maybe. If your top is installed normally using only silicone caulk then over time it will probably come loose and fail. In general 2/3 of any top needs to be supported but with such a small top that people will lean on even more would be needed to be supported unless it is epoxied to the wall in some manner. What did the granite installers tell you?

The granite installers were kind of back and forth. As you can see they but a small 2x4 underneath. My problem is I can not find a bracket that is only 5 inches.

If they used 100% silicone and it's also siliconed to a riser (small granite back splash b/w lower and upper countertop), you should be fine. It's not going to just fall off and break. It will show signs of coming loose over time.

Go online and shop for
Brackets. I feel
Certain you can find a bracket with a 5" top. Depending on the style you select, it could add much to the design of the room.

I agree, use solid crown molding as lali51 mentioned. That's definitely the way to go.

I would love to fine modern brackets. Any suggestions to where I should get online?

I doubt if you need brackets at all. However if you want them I would go back to your granite supplier and have some made.