A paradox I have had stuck in my head for a long time.

A star roughly 29.39 trillion miles away is dated to explode 5 years from now. 5 light years is roughly 29.39 trillion miles, so it takes 5 years to reach the star while traveling at the speed of light. Time slows down at the speed of light and 5 years at light speed would be 35 years for everything else. If I were to travel to this star at the speed of light to see it just before it explodes, would I get there before or after the star has exploded?

I'm sure you guys will find an answer.