How does the Flaming Sphere spell’s area of effect work?

The description of the flaming sphere in the PHB reads:

Any creature that ends its turn within 5 feet of the sphere must […]

Does this mean flaming sphere affects a sphere with a diameter of 15 feet (5 feet from itself, 10 feet towards either direction)?

Also, does ramming the sphere require placing the sphere at the location of the enemy directly, or will it still do damage as long as the creature is in the affected range of the spell?