I have an interview coming up. The max starting salary is $8K more annually than what I make. Should I shoot for the higher number in my interview? How do I sell it?

Also, the minimum starting salary is $3K /less/ than what I currently make, so I want to be strategic about this during the interview. The position is a job that I have a ton of transferable skills in, but in an industry I haven’t specifically worked in. Tips? Thanks!