I also have 5 AmEx credit cards and 3 charge cards, all but one opened since November. Here are open dates:

Blue Cash Preferred 3/13 instant approval
Gold Delta Skymiles 11/15 instant approval
MB Plat (charge card) 12/15 instant approval
Biz Gold Rewards (charge card) 1/15 instant approval
Biz Plat (charge card) 1/15 - went to pending, approved 2 days later (applied same day as BRG)
SPG Personal 3/10/16 pending, approved 2 days later after a rep called me to verify app

SPG Biz 3/20/16 pending, approved 2 days later (no call)
Everyday Preferred 3/20/16 pending, approved 4 days later (no call)