You cannot take someone's sole means of transportation in Florida, and you cannot touch homesteaded property. It sounds like you may have an uncollectable judgment in hand, which is why most attorneys wont touch such cases.
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Unfortunately, you cannot get the car, and even if you could, the judgment debtor could simply declare bankruptcy. I might consider settling with the debtor for less than the $5k, just to get some funds in your pocket.
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The judgment debtor is entitled to a specific exemption of $1,000 against the equity in a vehicle used for personal transportation. Additionally, if the judgment debtor does not own a residence, then they can take a statutory exemption of $4,000 against the equity in addition to the specific $1,000 exemption. Lastly, it is possible for the judgment debtor to apply most or all of a $1,000 wild card exemption for personal property that is afforded by our state constitution. If the vehicle is owned outright, then there may be a chance at recovery. But, if there is a bank loan secured by the vehicle it would get paid first, minus the exemptions (could by as much as $6,000 in total), could leave you with nothing to recover. Also, who ever advised you regarding the costs is correct. You would be responsible for paying costs to the sheriff, costs for the towing, costs for storage, and costs to advertise the sale. You need to recover your costs before you can say you recovered anything meaningful. As a final consideration, keep in mind that the vehicle may be worth $15,000 in a private sale, but at a sheriff's auction it might not sell for half that amount because of the risks involved to the buyer.
The law is complicated and although the facts expressed may seem to be all that is relevant, there may be many other important facts to consider. Also, the law is constantly undergoing change, so what may be correct today, may not be accurate tomorrow. Only a full consultation with an attorney experienced or knowledgeable in the specific legal subject matter is likely to result in the optimal course of action.