I'm super confused as to how what you did is correct, so I'll just explain it how I understand it:

We are trying to find cash flows from operations only, so just ignore anything related to financing or investing.

                                                                      N.I. $300,000

1. Eqpmt $25,000 increase  [Buying equipment is investing, so ignore]

2. Accumulated Depreciation $40,000 increase [this means we had $40,000 in depreciation expense.  We must add this back since it is an operating expense that did not reduce our cash]

3. Note Payable $30,000 increase [Issuing debt is financing, so ignore]

4. Sold equipment with Accumulated Depreciation of $12,000 for a gain of $5,000 [A gain adds to operating income, but this cash inflow will already be accounted for in the investing cashflows section, so we must subtract it to avoid double-counting.  Accumulated Depreciation means depreciation expense of $12,000, which we must add back].

5. Purchased $50,000 in eqpment w/ cash and a Note Payable (This is Investing/Financing, so ignore)

6. Depreciation expense of $52,000 [we already added this back by figuring it from Accum. Depr. (40k +12k = 52,000)]

Now just reconcile N.I.  300,00 + 52,000 - 5,000 = $347,000

 Hope this helps