Couple of websites listed below that address the 5th and how it pertains to civil lawsuits. There are evidently a lot of different rules that apply and to be honest much of this is over my head.
This one is less in depth than the next one but it also incorporates some Texas law in it so things might well be different in Florida.
A couple of paragraphs below the url. Lots more on the website:
http://judgebonniesudderth.wordpress.com/2011/09/26/use-of-the-fifth-amendment-privilege-in-a-civil-case/Of course, a witness’s right not to self-incriminate is found in the Fifth Amendment. (Article I, Section 10 of the Texas Constitution contains a similar provision as well.) This Constitutional right includes a defendant’s right to: (1) remain silent, (2) not be called as a witness for the prosecution, and (3) not have the fact that he exercised his right against self-incrimination used against him. This principle is well-established in the criminal context where juries are instructed that the defendant cannot be compelled to testify, and that if he exercises his right not to testify, the jury cannot use this as any evidence of guilt whatsoever.
In civil cases, however, the juries receive no such instruction. First of all, any party or witness in a civil case may be called to testify, whether they are facing criminal charges or not. Second, witnesses in civil actions do not enjoy an unfettered right to refuse to answer questions on Fifth Amendment grounds. Finally, in a civil case it is perfectly permissible for a judge or jury to infer that a witness is guilty of wrongdoing if they invoke the Fifth Amendment privilege against self-incrimination in response to a question. (Of course, civil juries can’t send witnesses to jail for invoking the Fifth Amendment; they can only find them civilly liable.)
This one is quite in detail and has many various examples of the 5th Amendment and how it may be applied:
http://www.sualaw.com/Appearances-Articles/Fifth_Amendment_Right_Against_Self_Incrimination_in_Civil_Cases.pdf
