First, before we talk about anything having to do with the credit score, we need the disclaimer that the exact credit score formulas are proprietary secrets that have not been revealed. Therefore, all we have to go on are broad generalities that FICO has given us.
That having been said, the credit card debt utilization portion of your score generally has at least two components: an overall utilization, and a per-card utilization.
Your overall utilization is taken by adding up all your credit card debt and all your credit limits and dividing. Using your numbers above, you are sitting at about 95%. The per-card utilization is the individual utilization of each card. Your five cards range in utilization from 69% to 100%.
Paying one card over another has no affect on your overall utilization, but obviously will change the per-card utilization of the one you pay first. So, to your question: Is it better on the credit score to have one low-util card and one high-util card, or to have two medium-util cards? I haven't read anything that definitively answers this question.
Here is my advice to you: The big problem you have is the debt, not the credit score. Your credit card debt should be treated like an emergency that needs to be taken care of as quickly as you possibly can. Instead of trying to optimize your credit score, you should be trying to minimize the number of days until all of your credit cards are completely paid off. The credit score will take care of itself once you get your financial situation back on track.
There is debate about the order in which one should pay off their debts, but the fact of the matter is that the order is not as significant as the intensity at which you pay them all off. Dedicate yourself to getting rid of the debts as fast as possible, and it won't matter much which order they get paid off in.
Finally, to answer your question, I recommend that you attack the card debt one at a time instead of trying to pay them off evenly. Not because it will optimize your credit score, but because it will help you focus your debt-reduction energy as you work on resolving your debt emergency. Fortunately, the credit utilization portion of the credit score has no history, so once you pay all of these off, the utilization portion of your score will get better immediately, and the path you took to get there will be irrelevant.
After the credit cards are completely paid off, and you have resolved never to spend money that you don't have again, it is time to work on the student loans....