Magnus...you will have absolutely no problems in the Bahamas with 5'10. And you'll be able to go to 95% of the places shoal draft cruisers go to.
As much as I love the Bahamas...if your goal is the caribe AND you and the boat are bluewater capable then your friends are right. Head out to Bermuda and then south for 10 days or so and you are there. (I did NOT do this and wish I did!! )...but friends have and the Caribe1500 out of Norfolk every Nov.1st or so might be a good way to do it.
I did the thorny path down through the Bahamas chain to T&C, DR, PR and Virgins and further south. It is a long hard slog with motorsailing against prevailing wind and waves for about 700 miles and frequent long layovers because conditions would not let us move. It took us about 10 days of ACTUAL cruising/motoring to get from GeorgeTown in the Exumas to St. Thomas...but it took over 2 months of actual time to do that due to the need to wait for NON prevailing weather! Don't think I'm chicken about conditions either....people at
anchor with us left and came back with their tails between their legs...you just don't understand what continuous 20Kt+ winds for a month in your face can do to sea state as well.
Now we LOVED everywhere we visited along the way EXCEPT Luperon,DR but it would be a lot easier to see it all with the wind at our backs on the way back home from the Caribe. We loved the Bahamas best of all (and i draw 6 ft.) so don't miss them one way or the other!! Good luck!