Wouldn't close anything yet and i'd garden for at least 6-9 months .. close to a year even......
Theres an ingredient your missing... its not just the score.... its age......Again. your score may be high, but its not very strong...
Meaning it won't stand up to scrutiny, either a UW or the automated type....
Really don't think its time for a spree yet... let some of those accounts get closer to a year old... know you want to try to get those fees to stop but you really want to think about that near month 11 not month 3-4....
Please reconsider..
At this point you don't need to close subprimes.. but youll want to closer to when they hit their 11th month before the one year fees kick in.
https://www.youtube.com/watch?v=W9ZD3_ppcPE
-J
+2
I was in your same boat and have two subprime cards. The Cap 1 I'm going to keep for now and is my oldest (one year this month). The other I'll be closing once that annual fee kicks in again. I've kept those accounts open and have paid on them consistently, PIF'ng every month, making multiple payments a month. Scores were likes yours...but waited until the one year mark and then apped. Was successful with two prime card approvals with decent SL's just a week ago (first two cards under wallet ↓). As above posters mentioned, age is an important factor when applying for credit. Anyone can have a credit card open for a month and make one payment on time. It's the longevity most like to see.
Don't close anything just yet and I would definitely garden for a bit if these accounts are as new as you say. Remember, if you app and get denied, you waste an HP. You also risk being denied automatically because of two many inquiries, assuming all those cards you have now were HP's and were done so recently ago (HP's take 1-2 years to completely fall off, depending on scoring model used by lender).
Just a suggestion....
Hope this helps 
@Anonymous wrote:+2
I was in your same boat and have two subprime cards. The Cap 1 I'm going to keep for now and is my oldest (one year this month). The other I'll be closing once that annual fee kicks in again. I've kept those accounts open and have paid on them consistently, PIF'ng every month, making multiple payments a month. Scores were likes yours...but waited until the one year mark and then apped. Was successful with two prime card approvals with decent SL's just a week ago (first two cards under wallet ↓). As above posters mentioned, age is an important factor when applying for credit. Anyone can have a credit card open for a month and make one payment on time. It's the longevity most like to see.
Don't close anything just yet and I would definitely garden for a bit if these accounts are as new as you say. Remember, if you app and get denied, you waste an HP. You also risk being denied automatically because of two many inquiries, assuming all those cards you have now were HP's and were done so recently ago (HP's take 1-2 years to completely fall off, depending on scoring model used by lender).
Just a suggestion....
Hope this helps
+3
Garden and dont close your cards let it get old at least 1 year
@pipeguy wrote:If it were me I'd close the Credit One account, but then again I never would have opened it considering the vultures behind that company.
I "get" the excitement of being approved for new accounts, but from your post, it looks like you just went on an app spree (1 month and 3-month-old accounts).
As others have mentioned, building a strong credit history is not a speed race and you need to think long-term in years rather than quantity over quality.
Would you rather have 1 or 2 universal use cards (MC/V/AE/Discover) with limits of $5000 or 10 starter or store cards with $300 to $500 limits? Although at this point you might be thinking quantity that will evolve into the quality of your cards over time, but if you think about it that way (better or prime cards you can use anywhere) you'll resist the instant gratification of "app sprees" for cards you'll end up closing or not using.
+1!!
I must agree with him on the Credit One card. I now wish I had never opened mine and am just thankful it's not my oldest so I can close it out without hurting my AAoA. Trust me, I understand the temptation of apping and the gratification received when you get that magic number and instant approval, but these things take time. I was highly tempted to keep apping earlier this week (felt I was on a role), but stopped after successful approval #2. Back to gardening for me.... I understand the process and have patience. Although, I realize not all of us do. However, I would heed the advice given here. I feel all the advice I was given was true and sincere and by listening to it (and continuing to), I've been able to succeed at what I want so far.
Good advice from everyone above! ↑↑↑ 
P.S. - Remember, we're all family here and only want to see all fellow forum members succeed. If you're interested, there is a Garden forum to cool down in and share your thoughts and frustration. UncleB maintains it and it's a great thing to be involved in! 
5 cards in 3 months, that's plenty of spree for now imo. If you give it a year, using your current cards to establish payment history your score will rise and you'll be in a better position to apply for what you want not what you can get