Final answer:
The item in The Binding of Isaac: Rebirth that grants +1.0 Damage Up and +5 Range Up to tears fired from Isaac's left eye is The Inner Eye.
Step-by-step explanation:
The item in The Binding of Isaac: Rebirth that grants +1.0 Damage Up and +5 Range Up to tears fired from Isaac's left eye is The Inner Eye.
The Inner Eye is a special item that causes Isaac to fire three tears at once in a fixed pattern. This means that two of the tears are fired from Isaac's left eye, and those tears receive the damage and range boosts mentioned in the question.
If you possess an item that causes all tears to be fired from a single source, there is a 50% chance that the effects of The Inner Eye will apply to all tears.