Kara purchases a home in Dallas, TX for $$400,000$ which she uses for investment purposes. After purchasing the home, Kara decides to make a few improvements, including painting the walls herself $($estimated cost of labor: $$500)$; hiring contractors to install a paver patio $($cost: $$10,000)$ and putting in a pool $($cost: $$50,000).$ Kara has now owned the home for $5$ years and took $$7,000$ of depreciation deductions each year. What is Kara's basis in the Dallas property? Explain your answer in full.