Healthy diet keeps you healthy, but it does not slow aging. It prevents death from reasons other than aging. To prove "slowing aging", you need to demonstrate

Healthy diet keeps you healthy, but it does not slow aging. It prevents death from reasons other than aging. To prove "slowing aging", you need to demonstrate increase in maximum lifespan, not average lifespan. Exercise, diet, etc. increase average lifespan. There is no evidence they increase maximum lifespan, none at all.