I am driving my car at the speed of light and I turn on my headlights. What do I see?
Seems we're both wrong. The person travelling (close to) the speed of light would see a normal beam of light but it wouldn't exceed the speed of light.
I love science but I never really know what I'm talking about because all I can do is repeat second hand information and form a vague and shadowy understanding based on the experiences of others, never knowing whether what I heard or read is true or even likely to be true. But then again, I think everyday life is a bit like that too, whether we realise it or not.