You don't provide enough information.
Your capital gain is the difference between the selling price and the cost basis. If the home was the main home where you lived at least 2 years and owned at least 2 years, you can exclude the first $250,000 of capital gain.
The problem you will have is proving what the cost basis was.
In your situation, your father owned 100% of the home in 2004, and gave you half the home in 2005. You inherited the other half in 2017. Your cost basis would be figured in one of two ways, depending on what the deed actually said.
In the simple case, if you were added to the deed but your father had a "life estate", that meant that you could not sell your half as long as your father was alive. So you weren't really given anything of value when you were added to the deed, and you really inherited the whole house, so your cost basis is equal to the fair market value on the day your father died. You can document this through a real estate appraiser who can do a backdated valuation based on historical records of sales of similar homes around that time. You can further increase your cost basis by any permanent improvements you made after you inherited the house in 2017 (like remodeling, replacing a furnace, etc.). Ignore the value of any improvements made between 2005 and 2017, since the stepped up basis covers all that.
In the complex case, you were given half the house "in fee simple" or as "joint tenants with right of survivorship". In this case, you were given half the house in 2005. You also get half your father's cost basis. Then you inherited the other half in 2017, and received a "stepped up" basis equal to half the fair market value at the time. For example, suppose your father's cost basis was $50,000, and the value in 2017 was $350,000. Your cost basis will now be $25,000 (the original basis on the half you were given in 2005) plus $175,000 (the stepped up basis on the half you inherited in 2017). You can still add further to your cost basis by any permanent improvements you made after you inherited the house in 2017. You can also increase your basis by half the cost of any improvements made between 2005 and 2017, since half the cost is applied to the basis of the half-share you were given in 2005.
Figuring out your father's cost basis will be the hardest part. In general, his basis would be half of what he paid for the home with your mother, plus half the value of the home in 2004 (since he inherited half the home from her with a stepped up basis). his basis would also be increased by half the cost of permanent improvements made between the time he bought the home and the date his wife died and he inherited the other half. If your parents lived in a community property state, your father received a basis equal to the full fair market value of the property on the day his wife died in 2004.
You can make some guesses, but it will be best to have documented proof of the cost basis. If audited, the IRS does not have to award any deduction or basis that you can't prove with appropriate documents. Don't send documents to the IRS, just file your return, but keep your proof for 6 years.
