Screwed out of $5000 by our real estate agent? or standard practice?

We found out a week before closing on our house that we qualify for a $5000 interest free loan from the city housing dept because we are in a low enough income bracket. If we stay in the house for 10 years we don't have to pay it back. Our real estate agent said that we have to close on Friday because that is... show more We found out a week before closing on our house that we qualify for a $5000 interest free loan from the city housing dept because we are in a low enough income bracket. If we stay in the house for 10 years we don't have to pay it back. Our real estate agent said that we have to close on Friday because that is how the sellers are going to pay the contractors who put in the new HVAC system and to pay for tenting the house for termintes. The sellers agreed to pay for all that. I don't see why we have to loose the 5000 loan/gift because the sellers don't have the cash to pay the contractors, even though our contract says it is their responsibility to cover those costs. It would only take 3-4 weeks to get this loan through.
My husband and I decided to just close on Friday but I am sick about it. I am not excited about owning our first house anymore and If we walk away from the house we loose $1200. help me feel better about this!!
Update: We asked our lender about this loan last month and she made a mistake and thought we didn't qualify when we do. There was no info about it on the city website when we checked for ourselves lat month. The house is only850 sq feet and we are asking for the HVAC because it had NO heat or air and that isn't... show more We asked our lender about this loan last month and she made a mistake and thought we didn't qualify when we do. There was no info about it on the city website when we checked for ourselves lat month. The house is only850 sq feet and we are asking for the HVAC because it had NO heat or air and that isn't legal. We are paying the asking price. No one is getting screwed here except us. These sellers are turning the house over as a gain. We are struggling to get our family into our first home. I'm so sick of real estate idiots who don't care about families trying to make it.
Update 2: The idiot is the real estate attorney saying I didn't do my homework when I did. I don't understand why waiting 3 weeks is deemed as more of a inconvenience than loosing $5000? What would you do/say if your kid was in my place trying to buy their first house?
Update 3: I don't want to "walk" because 1. I like the house 2. The sellers would be put in a terrible bind after installing the stuff then not having a buyer. I was hoping for some spirit lifting but I only got rude comments. I try to truly help people with my answers, not be hateful. People suck. Thanks... show more I don't want to "walk" because
1. I like the house
2. The sellers would be put in a terrible bind after installing the stuff then not having a buyer.

I was hoping for some spirit lifting but I only got rude comments. I try to truly help people with my answers, not be hateful. People suck. Thanks for nothing everyone.
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