How much will the capital gains tax be for selling off part of our land?

While the question is about capital gains taxes there are a few other things to consider before listing the property for sale.

We own (mortgaged) 15.44 acres of land which includes our primary home and improvements. We are considering selling off an unimproved section (5.5 acres) of said property.

That means that the mortgage covers the part that is for sale, and the part that you will retain. The lender will have to agree to this partial sale unless you are going to take other money you have to retire the entire mortgage. Even if they agree they have a mortgage lien on the property, and their approval will be needed to complete the transaction.

We are considering selling off an unimproved section (5.5 acres) of said property.

Make sure the local government allows this. Some locations have minimum sizes for property. In the county I live the there are sections that have a minimum 10 acre lot size. Even if they allow it, there will be a process to subdivide the property. Which also would require approval from the lender. Getting government approval could be trivial, or it could require a public hearing, or it could be impossible.

we are selling the 5.5 acres for 80,000. We paid 2,500. per acre for the land in 2006 but it is now worth aprox. 14,500 per acre.

The value of the land might not be uniform across the full property. The determination of the basis for the part you are selling will be very important, and if you are audited this would be one of the places they would review. The important thing would be documenting what it was worth for the unimproved land in 2006

We paid 2,500. per acre for the land in 2006

This is your basis.

we are selling the 5.5 acres for 80,000

These are your proceeds

The gain is the simple math: 80000-5.5*2500=66250. So $66,250 is the gain. The tax depends on your overall tax situation, capital gains tax is progressive

Additional expenses incidental to the purchase or sale transactions (legal fees, surveys, whatever) can be added to the basis if they're reasonable and ordinary for this type of transaction. Note that since you're only selling part of the property, you may need to prorate these expenses or allocate them to either the sold part or retained part, depending on the circumstances. For example, since the mortgage remains on the retained part, mortgage related expenses should probably be allocated to the basis of the retained portion.

You might need to engage a CPA/EA to properly report the whole thing.