Final answer:
To find the asset's remaining useful life, subtract the three years that have already passed from the total useful life (10 years) calculated using the straight-line depreciation method. The asset thus has 7 years of remaining useful life.
Step-by-step explanation:
The asset's remaining useful life can be determined using the straight-line method of depreciation. Given that the depreciation expense for the third year is $5,000 and the accumulated depreciation after three years is $15,000, we can calculate the asset's total useful life and then subtract the three years that have already passed.
The initial cost of the asset is $53,000, and the salvage value is $3,000, which means the total depreciation over the asset's life is $53,000 - $3,000 = $50,000. With an annual depreciation of $5,000, the total useful life is $50,000 / $5,000 = 10 years. As three years have already passed, the remaining useful life of the asset is 7 years.