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?
The sphere of fire from the flaming sphere spell is only 5 feet wide. So on a grid with 5-foot squares, it would affect a 3×3 area, with the sphere in the middle square. For ramming, the spell specifically says:
If you ram the sphere into a creature, that creature must make the saving throw against the sphere’s damage, and the sphere stops moving this turn.
This means you use your command of the sphere to move it directly into a creature's space (thereby hitting it) and they have to make a normal Dex save, and if the sphere hits the target before moving its full 30 feet you lose the rest of the move distance.
