Why is depreciable basis for a $5500 computer listed as $0/5.00 years ?

We can't see any of your details.  Purchases over $2500 must be depreciated although there are a number of methods available depending on your situation.

Is this for 100% business use, and are you using Turbotax Self-employment version for self-employment or a single member LLC, or are you using the Business program?  If this is shared use (partly personal and partly business use), how did you calculate the business use percentage and did you enter it correctly? 

It is possible you chose section 179 depreciation, which is limited to your net business income in the current year. That would result in $0 depreciation expense in the current year if your business operated at a loss. When you enter your asset, you will come to a screen that says How do you want to deduct this item? On that screen you have an option to take section 179 depreciation or other special depreciation allowance (SDA). You may have chosen to section 179 depreciation. If so, you can go back into your business entries and update your asset/depreciation entry to change your choice.

The special depreciation option will give you a deduction  even if you have a loss from the business in the current year. You find the depreciation options by updating your business entries and on the screen that says Your (name of business) Business, choose Business Assets, then Assets being depreciated. Update that section and choose I want to go to my asset summary. Once on the asset summary, edit the asset and scroll through until you come to the screen that says  How do you want to deduct this item? You can make your depreciation elections on that screen.