Is it too late to contact the debt collection companies and try to work something out?

No. If they're debt collection companies and the debts are 4 to 5 years old, your $5k debt cost them less than $200 to acquire. I would say something like "Look, I'm unemployed and looking at several different companies who all want more money than I have. I'm making this same offer to three credit card companies this week: $1k paid immediately in return for full satisfaction of this debt. I will understand if you feel the need to reject that offer and sue me, but I have no assets. This represents the best deal you're going to get."

Do this negotiation entirely on paper, delivered in the postal mail, with return receipt requested. Don't talk to anyone on the phone for longer than it takes to say "What is your postal address?" Your first letter to each company should include language similar to "It is inconvenient for me to receive debt collection communications via telephone or any other means but postal mail. This letter constitutes written notice under the Fair Debt Collection Practices Act that you are not to contact me about this matter via any method other than the postal mail."

Our overarching strategy here is avoiding having folks sue you (n.b. the process server is in play because someone is already suing you, and merely ducking him will not make that impossible -- they'll just put a notice in the newspaper and the judge will certify "service accomplished by public notice"), because you'll probably not go to court in time to contest and if you do contest you'll likely lose (you do, after all, owe this money). You will then have a default judgment entered against you, for the entire sum you borrowed plus interest plus collection costs and legal fees. This will likely be more than double the amount you think you owe. The debt collection agency will then begin contacting every bank/etc in the area to see if you have an account and then seize the contents to satisfy the judgement. If they don't recover 100%, they will petition -- and receive -- a court order to garnish your wages for the next several years until that amount is satisfied.

This process will be stressful and costly for you. It is highly in your advantage to avoid it. Ignoring it will NOT make it go away.

I can probably swing a 1k down payment and the rest over monthly payments for a year to a year and a half.

I would suggest that you be Very Darn Sure (TM) that you can actually handle this this time, because if you get to month 7 on one of those agreements and then miss a payment by even a day, you're in a situation which will be in every possible way worse than the situation you are in today. You should strongly prefer paying part of your debt today in full satisfaction versus a payment plan. They will suggest payment plans, because that gets them some money and because probabalisticly you like virtually all other debtors will default on that payment plan, after which point collection costs will inflate the debt to a number at least as large as the number they are claiming now.

There's also the additional issue that I may have exaggerated my freelance income somewhat on the applications.

I am not a lawyer, but to the extent that you trust me: you have nothing to worry about with regards to this.