Your answer is incorrect because you're using net annual cash flow, which includes depreciation. However, depreciation is a non-cash expense and should not be included in the calculation of cash payback period.
To calculate the cash payback period, you need to use the net income increase as your net annual cash flow, which is $5,000.
Cash payback period = Cost of capital investment / Net annual cash flow
= $48,000 / $5,000
= 9.6 years
Therefore, the cash payback period is 9.6 years.