Adjusted Cost Basis-Permanent Improvements-If insurance company paid, minus deductible, Can that be counted as a permanent improvement?

Your basis has to be reduced by the insurance reimbursement.

So for example, so something was damaged and the Insurance claim was $20K less $5K deductible.

You had it fixed and it cost, $22K less what insurance paid ($15K) your basis in this is now $7K.  This $7K depending on what it is can be counted as a improvement for depreciation purposes.