This is tough, assuming we can't have things that would make it easy to leave the island (such as a ship anchored offshore) or that are impractical to leave on an island (such as, say, a house or a large machine). I assume a full set of clothing including outerwear (such as a jacket) and headgear (such as a hat) is included by default, i.e. it is not one of the 5 items.
I'd likely have the following (and I assume that for things like firearms it includes the standard accessories I would normally have, such as a means to carry the ammo the OP says is automatically included):
1. Vierling [(12ga.X12ga.X.22LRX.30-06 or .303) equipped with a shooting sling and having a buttstock designed to hold a small survival kit (included) and ammo onboard; ammo includeds 12ga. flares)
2. A very long length of rope of a thickness suitable for multiple purposes including building structures or camp devices
3. A good quality fixed-blade knife suitable for use as a tool or for hunting
4. A canteen set (pouch/1qt. canteen/canteen cup)
5. A large amount of clear plastic sheeting
I really wanted to include some sort of firestarting device (such as a lighter or something that does not use fuel), but ultimately it is easier to make a fire without tools than to make enough suitable rope for various needs.
I also wanted to include a Nook and a portable solar panel to charge it so I can have a pasttime and also have books that contain references useful for survival, building things, etc., but the above things are more important.
I also wanted to include something to write with and on, and I am not sure if having clothing by default would mean also having the usual things we carry in our pockets (which means I would have a pen and/or mechanical pencil, Rite-in-the-Rain pockt notebook, keys, CPR mask with one-way valve, Victorinox Soldier, Victorinox Officier-Suisse, a Bic lighter, a small wallet, a cellphone, a bluetooth device, and a coin purse with coins), in which case I wouldn't have to worry about that.