See if you can can book through Gatwick Connects+ - that way you'll have a protected connection which would be ideal.
Even if you don't book through them, you can still use the Gatwick Connects bag check service which saves some hassle. 4-5h shuld be plenty - easyJet offer rebooking for a reasonable £80 rescue fee too in case you don't make it. Not sure about WestJet for the return though - that's where booking the protected option would be safer if possible.
http://www.gatwickairport.com/at-the...twickconnects/