At present I would not obsess over the track taking it toward Florida.

First, this is 5 days out. In hurricane time, that is a very long period. Hurricanes are erratic and hard to predict past about two days.

Second, my rule of thumb on tropical cyclones: give 12 to 24 hours after a tropical storm is declared for model runs to do a good job with the tracks; give generally 12 hours after an significant strengthening of a cyclone to get updated model runs with the deeper storm. Based on this, it will be sometime tomorrow (Sunday) before we really get a good handle on the storm's track.

This is heavily due to the fact that model runs take time to run, with the GFS / NOGAPS outputting every 6 hours data ingested 6 hours earlier, and the GFDL / GFNL running every 6 hours base on the output of various global models. This means that the minimum time before the GFDL / GFNL shows a run that ingested the current storm data (specifically the hurricane hunter recon data) is at least 12 hours from now.

Third, if the storm does stick to that track, it will pass over the mountains on Hispanola. It will be substantially weakened by that.

Fourth, if the storm strengthens, and thus deepens, the track will likely shift toward the right, making it more likely to miss Florida (but not guaranteed), though that does open up other east coast targets.