Hello mate, 5mm isn't too bad though outside of BS recommendations. I have never laid slate yet and I know "it" is probably not flat so don't know if levelling would really solve the problem.
I think most of the more experienced guys on here would recommend that BAL PTB flexible be used for this type of installation but I understand it can be a little tricky if you haven't used it before. It can be used in a bed up to 25mm so would easily fill your problem area.
Have a look at this data sheet from BAL:
http://194.223.92.131/pdf/Technical%...B_Flexible.pdf
Grumpy