I'm not sure about the sneezing but I know with my daughter she had hiccups ALL THE TIME! lol. The whole last month of my pregnancy and the first month or so after she was born. I mentioned it to her pediatrician and she said it was normal for some babies. I can't remember exactly what he said caused it, it's been a few years, but I want to say something like specific nerve is more active in some babies that causes hiccups more frequently. Eventually the stopped happening so often.
This is your first baby, she's five days old. She's still brand new, but if it will put your heart at ease, call her pediatrician, and ask those questions. You could also ask Mom, Grandma, or any other learned Mother in your family for help and advice.