You can do it. I'm not that good and I ran the 10k and 5k the same day in a one day conference meet (it was a small school conference and I was fortunate to win both/tied with a teammate in the 5k). The 10k was late morning/noon and the 5k was about 5:00 or 6:00. The 5k was very tactical thankfully so the pace wasn't an issue and most guys were doubling back and tired too.
In your situation you can get a couple good ice baths, plenty of hydration, protein, stay off your legs and out of the sun. And remember chances are by the time the 5k rolls around Sat afternoon/evening most of the guys will be tired too. Conference champs 5k's are rarely that fast relative to the fields PR's, etc. Just do an easy run 20-30 min on Friday to shake out the junk and a light shake out run Sat AM.
Be thankful you're not running that double at nationals. In some divisions you run a 10k on Th night, 5k semi on Fri and 5k final on Sat. Talk about a war of attrition.
Number one key...mental preparation for the challenge! Go for it! All the best.