Can my son's mother take him without custody arrangements?

Generally, in the absence of a court order establishing paternity, you don't have any legally recognized rights with respect to the child. However, the fact that he has been residing with you for the last five years will help you with your majority timesharing claim, but you need to file a paternity action and an action for return of the child under Florida's relocation statute as soon as possible. Do not just show up and take the child, it could result in your arrest and other complications. Consult with an experienced attorney to discuss the specifics of your situation and your options.

Have you filed a paternity case? You might want to think about doing that. Yes, she can take him without custody arrangements, and no you cannot do as you ask without legal ramifications.

If you have never had your legal rights as the father adjudicated in court, then the answer is NO, you cannot just go and get him. In Florida, custody defaults to the Mother until your rights as the legal father are established by a Judge. Only then do you have equal rights with the Mother. You need to hire an attorney and file an action to establish your legal rights after which custody and visitation will be determined.