Drew,
Here are three strategies that you can apply:
1) Lease-Purchase Option: Ask the seller if they will rent the house to you for one year, and after you've qualified for a credit score, you will purchase the house at the agreed price (be prepared to offer to purchase the house at 2 to 3 percent above the current agreed price to account for appreciation; however, save this price increase until later in the negotiations, if it is needed to sweeten or close the deal). Tell the seller that you will pay for the option of purchasing the house at the end of the period for the agreed upon price, and ask them how much they'd be willing to take to give you that option. I think $5000 is too much, at least to start your negotiations, and I recommend you do not exceed that--as it's a huge portion of your gifted nest egg. Instead, offer about 1 to 2 percent of the purchase price ($800 to $1500).
As a previous poster mentioned, you want to ensure that this option is counted as part of the down payment when you close. However, also make sure that you and the seller both understand that if you don't complete the agreement and purchase the house, then the seller gets to keep the option because you have taken the house off the market. Ask the seller how much his current mortgage payment on the property is, and then offer to pay enough rent to give him a positive monthly cashflow of $100.
Also, point out to the seller that because you intend to purchase the house--make this point often--naturally, you will take care of it with the same "pride of ownership" as any other home owner, so the seller shouldn't worry about the place becoming run-down while you are leasing it.
2) Rent-to-Own: Instead of paying an option, offer to pay $200 to $300 above market rent for one year, asking the seller to count that monthly overage as part of your down payment. So, if comparable market rents are $700/month, offer to pay $900 to $1000/month for one year. At the end of a year, you'll have $2400 to $3600 paid towards a down payment--the seller doesn't have to keep it in escrow, but will account for it at closing. Follow the same timeline as the first strategy. In this scenario, you also may offer to pay an option, thus creating a hybrid of the lease-purchase and the rent-to-own strategies. Again, the option you pay should be counted towards your down payment.
3) Owner Financing: On a different tack, ask the seller to finance your purchase, or perhaps just your down payment (thereby saving your Grandmother's gift for some other purpose, or combining it with the seller financing to lower your bank loan amount). Offer the seller 6 to 8 percent interest, annuitized over 30 years, and be prepared to offer it as an interest-only loan, if necessary to sweeten the deal. You also can combine owner financing with the first two--ask the seller to finance your down payment when you close in 12 months. The seller actually receives more money for their house (in the form of interest and/or principal), and the tax bill for the sale of the house will be spread out over a longer period of time, saving the seller more money. At the end of the year, when you will have the house in your name and a good credit score, walk into a bank and re-finance the house with a lower interest loan and pay off the seller.
IMPORTANT: in all of these strategies, make sure you have contracts written up and give them to a title company and have them recorded to protect your interests. Also, if you use strategy 1 or 2, ensure that the seller agrees to keep records of your timely payments, which will help establish your credit score, mark you as a responsible payer to the bank, and which the bank will require to show that you actually paid above market rent and/or the option in the amounts being counted by the seller as part of your down payment.
I hope these help and I applaud you for getting into the real estate investment arena at a young age!