I finally got a job offer! Should I always counter the salary especially in this environment?

I've been looking for a new job for months. I currently work in a QA role that's hourly and I've been looking to transition to a job out of a production environment. I finally got a job offer today. It pays 60k a year, has 401k, and covers 100% insurance. However, it's only 5k more than what I currently make. I told them during my interview I was looking for a pay range between 60-70k and they went to low end. Should I counter? I don't have direct experience with this kind of role and the role is new. It's a mid sized company.

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