Thank you for your question.  The best way to determine whether or not a spider is a brown recluse is to check the number of eyes and the pattern of eye placement. Unfortunately, your photo wasn't enough of a close-up to show the necessary detail.  

The normal range of the brown recluse barely extends into the tip of the western panhandle of Florida, so they are not normally found in your county of Indian River. It's possible that an individual could be transported into the area by someone who was visiting an area within the brown recluse's normal range and the spider hitched a ride in camping gear or in a box that had been in storage, for example.  

The legs of the brown recluse have fine hairs, but not spines. The spider in your photo appears to have some spines on its legs. I don't think this is a brown recluse, but without being able to check the eyes, I can't be positive. 

Here's a link to an excellent website at the University of California, Riverside on the brown recluse.  It's written by Richard Vetter who is the author of the book The Brown Recluse Spider, an excellent resource for information on this species. This site provides accurate information on the brown recluse, and, since you saw the actual spider, you may be able to tell if your specimen matches the description on this page.
   
http://spiders.ucr.edu/recluseid.html

Sorry I can't be more definite, but without being able to count the eyes and check their arrangement, I'd just be guessing. Thank you for contacting Ask an Expert, and I hope this information provides some help.

Jim