2 out of 5 year rule

contract means nothing. starting on the date you closed on the purchase and ending 5 years later which if you closed on the purchase on 12/10/19 the 5 years ends 12/09/2024. You can close on 12/10/2024 because the 5-year lookback period for ownership and occupancy starts the day before closing.

did you depreciate the property when it was a rental? if not, you may want the services of a tax pro because the law requires that you reduce the basis by the amount of the depreciation that should have been taken while it was a rental. any gain based on that reduced basis is subject to section 1250 recapture. the depreciation recapture applies before the home sale exclusion.

 repairs do not add to your tax basis only improvements. 

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there is no way to avoid the depreciation recapture and if you wait past the 5 year mark you lose the home sale exclusion.   waiting until the last day to close is foolish. sometimes closing fails and then you would lose the $250k single or Married filing separately / $500K married filing jointly (assuming both meet the 2-year occupancy test) exclusion.

To be more specific, which to me seems to simplify it better, you must have lived in the property as your primary residence for at least 730 days (2 years) of last 1826 days (5 years) you owned it, counting back from the closing date of the dale.

I'm sorry but you have several problems here.

If the home goes under contract by the 10th do we qualify for the 2/5 yr rule or must it close by Dec 10th?

You must close by 3 years (1095 days) from when you stopped using the home as your main residence.

We only deduced expenses including repairs and maintenance on the home during the 3 years.

This was a mistake.  You should have claimed depreciation.  When you sell the home, you must pay depreciation recapture on the depreciation you took or could have taken.  Depreciation recapture is taxed at a higher rate than ordinary capital gains.  If you want to claim the depreciation deduction to get some retroactive tax benefits, it is too late to file amended returns since you used an improper depreciation method.  You must file a form 3115 to fix the depreciation, and this form usually requires professional assistance.  It is not included with Turbotax.

If we sell the home after this time how are we affected by the rule?

If you sell more than 3 years after moving all, all the gain is taxable.  Long term capital gains are taxed at zero%, 15% or 20% depending on your other income and filing status (a bit less than the tax rate for ordinary income).  However, the part of the gain that is due to depreciation that you should have taken will be taxed as ordinary income at 12%, 22% or 24%.  

Because you would have a taxable capital gain, it might be a good time to sell other capital property that has resulted in a loss, because you can deduct the loss against the gain (like stocks or other investments that have lost money).  

Looking to understand if best to hold on to the house or still sell if after Dec 10th. and to avoid capital gains taxes if possible. 

Because you have moved out, you can never avoid capital gains even if you move back in.  This creates a situation called "non-qualified use."  As an example, suppose you bought the house in 2018, rented in 2020, moved back in 2023, and sell in 2025.  Even though you would meet the 2 year rule in 2025, the rental period is non-qualified, and the gains attributed to that period of ownership are not eligible for the exclusion.  In that example, you owned the home for 7 years and lived in it for 4 years, so 3/7 of the gain is non-qualified and fully taxable, and 4/7 is qualified for the exclusion.