7 years in most cases, but…
Most derogatory accounts fall off your credit report after 7 years, with some exceptions. How old are those collection account? Are you sure that’s the reason for your low credit score?
If they are from the past two years than this may explain a low credit score, but if they are older than you’ll need to look for other reasons such as high utilization, late payments etc.
More than 70% of your credit score is made up by information from the past two years, so I doughty if those collection accounts are you main problem.
My advice is to try and negotiate some sort of agreement with the collection companies and pay off those debts. If they are old then you can negotiate a payment of 20%-30% of the original amount.
Most lender require now days that you pay off any outstanding debts before they approve you.