Will this fit my car's headlights?

Only if your car uses D5A HID bulbs from the factory. Check the bulb type on the old bulb or the owner's manual before ordering. It is not a fitment for halogen or other HID types.

Is 5000K brighter than the stock bulb?

Color temperature is not brightness. The gain comes from running 35W instead of the 25W many factory D5A bulbs use, which raises total light output. The 5000K rating describes the white color.

Do I need to replace both bulbs at once?

It is worth doing both sides together. HID bulbs dim and shift color with age, so a new bulb next to an old one can look mismatched in brightness and tint.

Will these work with my factory ballast?

They are built as a direct replacement for factory D5A HID systems, so they are meant to run on the existing ballast and wiring. The higher wattage is the main thing to weigh against your car's original setup.

Is this legal on the road?

The bulb is stated as compliant in arc position and size. Legality still depends on the housing: HID bulbs belong in HID projector housings, not in halogen reflectors.