Properly stored garlic can last up to six months, but it is important to remember that sprouted garlic indicates that its core is already breaking down and therefore sprouting.
When garlic is the main ingredient in the dish you are preparing (or at least one of the main ones), do not use sprouted garlic, as the sprouts will greatly bitter the dish. Really bitter!
If you use garlic only as a spice, you can cut off the sprout and the core is still usable. Trimming the garlic won't make you sick, but it's true that its potency is significantly reduced. Sprouted garlic has less than half the nutritional value compared to fresh garlic.
Another thing to know is that sprouted garlic is also a sign that it has been exposed to warmth, sun, and moisture for too long... You won't have any of these dilemmas if you avoid sprouted garlic.