[Marwan]

Ole, your profile doesnt say much about you, but i feel that you might not have tried spearfishing before, not so sure about long distance swiming either.. i may be wrong..
1 - Have you tried a 10KM swim before , in seas with currents, surf etc...?
2 - Have you tried spearfishing before?

The way i see it if your answer is NO to both or one of these questions, then your quest would be more long term then immediate..i would imagine that you would be taking A VERY BIG RISK, trying this now or later for that matter..versus going with a boat or maybe a kayak..
I say start with getting long fins used for freediving like omer ice fins which are especially good for long surface swims..learn how yo use them first and train for long distance swims...to reach a 10 KM swim comfortably in a pool, you are talking about several months of training
2- Start learning some basic freediving and spearfishing techniques..use resources from here on deeper Blue there are many...but the golden rule is TAKE YOUR TIME and PROGRESS IN SLOW STEPS...
3 - Start learning the area a bit more, i dont know how practical that is...are the reefs only 5kms away or are there closer ones, that you can start with? once you learn about the area and species, you get an idea of the kind of gun that would work
4 - Shark repellents, maybe a shark shield (look it up) but thats been debated too as being ineffectve at times, it would be your best bet maybe, or a power head that would fit on your spear...
5 - The dangers youre up against are not mainly sharks in my opinion...i can see a lot of dangers in your scenario having more to do with things like, fatigue, dehydration, muscle cramps, sea currents,hypothermia and yes sharks, all could be fatal..if you consider the time it will take to swim 5km spearfish and get swim back 5km draging fish, float etc.. if anything happens to you or your mates during that time, youre pretty much messed up...
6- to avoid any inconvenience like broken rubber band, mask strap, spear etc... you will need to be packing a lot for such a journey, water, food spare stuff, which would add considerable difficulty to the already very chalenging swim

I just hope im painting a more realistic picture and the things you need to consider if you are going to attempt this, and my final advice is to really get a boat or if you dont want any engines, try paddling across with a kayak, if conditions allow for that..
hope you make the right choice here and use a boat
Cheers mate and be safe..