If an offer made to purchase real estate from the heirs of an estate, via letter from attorney, is accepted via letter from the estate's attorney, can one of the heirs "change his mind" and refuse to sell? Does the purchaser have any legal recourse in enforcing the acceptance letter?

If the letter contained a reasonable description of the property (such as an address), a purchase price, an estimated closing date and the names of the buyers and sellers, then you may be able to enforce the letters as a contract. Speak to a real estate attorney in your area to see if you have a case.

Real estate and auto purchases have added specific requirements in each state. ( assuming this is in the US) You did not mention an exchange of money with the acceptance letter. Also depending on the state there would have to be a specific legal contract signed. Also if the purchase is in some states, the contract is not valid until there are lead paint, pest control and other inspections or wavers. So it is going to be very specific to your state, and also very specific if you sent a depoisit with the acceptance letter.

Also is the attorney for the estate the exector of it, or did he have a legal standing to agree to the sale.

You will have to have a local attorney review all of this, but normally unless there is an exchange of money, the contract has not been made.
It sounds like what you have is an agreement to write a contract but no specific contract was written. But again this is just an very open opinion based on some very general rules. Your state may or may not have specific laws.

We did place $5000 earnest money in the trust account of our attorney and he specified that in the offer letter. The attorney for the estate named the executor and stated that he accepted the offer. The property is in Tennessee and is farm land only, no structures. No specific closing date was set, just that closing would be as soon as the offer was accepted and the attorney for the estate could prepare the deeds/ppwk..

When you say that closing would be set as soon as offer was accepted,
Was this yours acceptance,or was this what you said when you sent in the money.

Makes a big difference.

But if they said that closing would be set upon acceptace and you send money to bind, ( and they did not notify you to cancel offer prior to receiving your money) it sounds like a binding contract to me.
I am not up 100 on TN.