Yes — the sentence is grammatically correct.
Step-by-step for a 5-year-old:
- "The zebra's black-and-white stripes" means the zebra has stripes that are both black and white. The hyphens in "black-and-white" are correct because those words together describe the stripes.
- "Confuse predators" means the stripes make animals that want to eat the zebra not know where the zebra is going.
- "And repel insects" means the stripes help keep bugs away.
Some simpler ways to say the same thing:
- "A zebra's black and white stripes confuse animals that want to eat it and keep bugs away."
- "Zebras have black and white stripes that scare away predators and stop insects from biting."
If you are talking about all zebras, you can also say "Zebras' black-and-white stripes..." or "Zebras have..." but the original sentence is fine as it is.