Jacks Mommy welcome to the boards
I have just had a look at your routine, I think the best plan of action would be;
Treat the 5am feed as a night feed and put your LO back to sleep and wake him up again at 6 or 7am (or whatever start time your want to go with). if you are too continue with a 5am start, his bedtime needs to be earlier as well.
Your feeding times will be; 7, 10, 1, 4, 7, DF and your 1 nightfeed. If after doing this you find he isn't hungry for his 7am feed after feeding at 5am, either limit the 5am feed so it just sees him through to 7am or give a full feed at 5am and topup at 7am, until he is developmentally able to last out until 7am with no night wakings.
I would class your 5am feed as a night feed, not necessity a 6th feed. I believe the book is referring to daytime core hours of 5 feeds plus a dreamfeed.
On a 5am start your feeds would be 5, 8, 11, 2, 5pm + DF, bedtime should be 1730/1800 as you are looking to achieve a 12 (ish) hr day.
However saying all of that if this EASY routine is working for you, stuck with it. EASY is a flexible routine and designed to suit around your lifestyle, as long as you follow the EAS in that order it will eliminate any feeding to sleep - don't feel you have to follow the feed times by the book, they are a guide only.
Your doing a brilliant job!!
HTH's