Is it illegal for a 16 year old to be left home alone overnight for 5 to 6 nights out of the week?

The parents of a child (i.e. someone typically under age 18) have certain legal obligations to care for them. In other words, a person with such parental responsibility has the legal duty to protect, house and provide for them.
Accordingly, virtually all states have some form of statute criminalizing the child neglect and abandonment (e.g. child endangerment laws). 
In FL, "neglect of a child" is defined as "a caregiver's failure or omission to provide a child with the care, supervision, and services necessary to maintain the child's physical and mental health, including, but not limited to, food, nutrition, clothing, shelter, supervision, medicine, and medical services that a prudent person would consider essential for the well-being of the child..." 
Since a 16 year old is still considered to be a "child" (i.e. minor), then leaving them at home unsupervised for days at a time may well constitute neglect under state law. However, since you gave no further details of the situation, you should consult directly with an attorney in your area or speak with your local social services department for further information.