How can I hang a 5ftx10 in plywood board that is 1/4 in thick?

Frame it..............

you could use large mirror hanger

Have you considered making a supportive frame from stronger lumber and nail it to the back of your plywood, or even nailing strips of wood across the length since that is where it is bowing.

Home Depot has 6' strips x 3.5"x 1/2", I bought 1 yesterday for $3.47, using it to replace a fence slat. They will gladly cut it down to the length you need. A couple of them should do the trick.

Best to you and your sister

sorry that it's not flat but might try a french cleat due to size and weight (google it)

No the stews go into the wall n the plastic clip part holds the art.