Hi George, thanks for considering a premium membership. :)
The Platinum membership does include 5 Chess Mentor lessons, I'm sorry for the confusion. And I am seeing the PayPal option on the upgrade page: http://i.imgur.com/X7G2V0c.png Are you not seeing this after choosing the option you wish?
I get the page https://www.chess.com/checkout/cart from the page
http://www.chess.com/membership?c=navbar#
George
KP to staff, my issue had not been resolved. I can not sign up for preminum membership using Paypal! The only option I get is to use a credit card and there is no way to get past the screen without putting in a credit card number. 
Problem solved, thank you.
I am trying to sign up for Platinum membership and found that:
1) Despite the FAQ there is no Paypal option on the checkout page.
2) When I attempt to sign up for Platinum membership I get a dialog box that says Chess Mentor is not available for Platinum membership if I want it I need to sign up for Diamond membership. According to the chart Platinum membership incluses 5 Chess Mentor lessons a day.
I'd prefer to to use Paypal rather than credit card and want the 5 Chess Mentor lessons.
George