Several people here are telling you that the ex has a shot. I don't particularly agree with them, but I want to trace the legal pathway that she's likely to take:

Step 1: Presumption of paternity under 257.55(d). Ignoring the gender language of the statute, the ex will likely argue that she held out the child as her own for five years. Why bother with a presumption of paternity, you ask?

Step 2: She'll want to file a motion for parenting time under 518.175(a). She'll have to do this because, in Minnesota, "visitation" isn't granted to just anyone who claims an interest in the child's life, unlike what others in this thread seem to be saying. Visitation can be granted to: (1) parents or (2) grandparents. People can also file for third party custody, but that doesn't seem to be what's going on. (Before you ask: TPC is difficult to obtain when the actual parent(s) are competent and active.) She'll want to get a presumption of parenthood first.

In cases like this, where there are allegations of abuse, the judge would likely assign a Guardian ad Litem to your case. The GAL would make recommendations on parenting time based on interviews with the child, the mother, and the ex. The judge might also order the parties to a social early neutral evaluation, or to participate in a parenting time evaluation.

All of these evaluations are to determine what's best in the interest of the child. If the ex is a manipulative bitch hellbent on exacting revenge through legal action targeting the child, it's going to come out in a recommendation at some point from someone. The ex will have wasted everyone's time, and likely everyone's money. But who knows? Maybe this person isn't terrible, and there's a strong parent-child bond there. But based on this one-sided presentation of facts, it's pretty clear that this is going nowhere.