What kind of switches do I need?

I would go with the light systems that you can control from your smart phone. I have seen them in many different places, such as Best Buy.

The only way I know of is with a x-10 switch that allows WiFi remote. Home improvement stores also carry different kinds of automated systems.

Never heard of a light or outlet that can be controlled from 5 different locations. Do know that a 3-Way light is only controlled from 2 different locations and has to be wired with special 3-Way wire which is different sire than is used for all the normal lights and outlets. Good luck with getting an answer.

a six way switch....That's right 6 way

You could also get one of those motion sensing systems or LED bulbs that automatically turns lights on when you come in the room and off when you leave. https://www.amazon.com/s/ref=nb_sb_ss_i_6_16?url=search-alias%3Daps&field-keywords=automatic+light+switch+sensor&sprefix=automatic+light+%2Caps%2C278&crid=M1JZV5H1DABU

Call and talk to an electrician. Wire will have to be connected to the existing light then fished over to the locations where you want the new switches to be cut in, hooked up and installed.

You would need a combination of 3 way and 4 way switches. Here are a bunch of wiring diagrams. You can also check with Home Depot, Lowes, or Menard's electrical department and they should be able to assist you.

https://www.google.co.in/search?q=wiring+in+4+way+switch+from+existing+3+way+switches&sa=X&rlz=1C1PRFE_enUS711US711&biw=1600&bih=770&tbm=isch&source=iu&pf=m&ictx=1&fir=H5jI7MrpEEkM1M%253A%252C5oATQ-1mCXoQ3M%252C_&usg=__2lvCXQAGX-O32wJLSkZSRmPRKmI%3D&ved=0ahUKEwiM6Zb91OzWAhUn0YMKHZc5C4cQ9QEITDAH&gws_rd=cr&dcr=0&ei=8bRHWuDSOcmNvQSU2KOADw#gws_rd=cr&imgrc=_