No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
3 credit cards is a good place to start rebuilding. You will see a maximum boost in FICO from just having 3 credit cards. When you get #4 and #5 you will get a FICO ding initially for the new accounts but after a year you'll have a stronger score from 5 credit cards. I wouldn't open a new one yet...
First, what is your BALANCE on each card? Post the credit limit and the balance on each. I bet that's what's hurting you.
The first thing you want to try is to do the AZEO method: All Zero Except One.
Pay down 2 of your cards to $0 and keep them there for statement cut. Keep in mind that some cards will post new interest on statement cut date so it may take 2 statements to post a true zero.
On the third card, pay it off EXCEPT for $5-$10 for statement cut. You want all your cards at ZERO, except for one, which has to be more than zero but less than 9% of the credit limit.
This can boost your score 10-20 points.
As long as you have 1 installment loan reporting and 3 credit cards reporting, doing AZEO can boost your scores nice.