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Time does indeed help, but it doesn't necessarily work in a very gradual way -- where you get a little increase every month. You might be stable for six months or a year and then get a bump.
The key thing though, is that you have a desire for your scores to go up. Can you tell us....
How many credit cards do you have?
Do you have any open installment loans?
Do you have any derogs? (Lates, chargeoffs, collections, etc.)
There may be a better way to get a score increase than just by time.
I encourage you to chat with as many people as you can (including google) about tips and tricks for removing medical debt from your reports. See if people in the rebuilding forum can advise you, do searches, take conversations into 1-on-1 private messages, etc.
Have you ever seen a documentary about African wildlife? The hippo often features in these. If you were to change the last vowel in its name to a different vowel, you'd find a word that some people find helpful with the issue of medical debt. Add the new word to your google searches and I am told that it might reveal some possible avenues. I know very little about the issue of medical debt and credit, and am actually restricted from the myFICO forum terms to discuss certain strategies even if I did. But certainly you should in a relaxed way be gradually looking into as many ways as you can of getting all your derogs off.
As far as the 5k personal loan goes -- this is a loan you are thinking about taking out because you actually need the 5k, right? Not because you think it will help your credit score?
There is a kind of loan you can take out (a $500 share secure loan from Alliant) that would help your score a good deal (20-30 points?) and it will cost you almost nothing in interest. But you do it purely for its scoring benefit -- it really doesn't get you any real money you can use. And once you add the 5k unsecured loan, all the benefit from the Alliant loan would go away.
The number of cards you have right now is fine. Adding more won't help especially.