Heathrow ?
 

Frankly no
Are you on the same ticket, or two seperate tickets, if the latter then no, if the former then you have a back up

Part of it depends upon which terminal you arrive on the flight from Edinburgh, and which terminal your flight to the US departs from. It’s easy to walk through the underground tunnel between terminals 2 and 3, but terminals 4 and 5 are on the opposite side of the runway.

Which airline is your flight to the States? If it is on BA and on the same ticket and your EDI flight arrives on time, that should be fine. ANY other permutation -- different airline (which means a different terminal), separate tickets (if you have checked luggage) , delayed arrival, etc, not a chance.

If all on BA but on separate tickets and you have checked luggage, you have a huge problem. Typically BA won't check bags through on separate BA tickets so you'd have to collect your bags go landside, and re check them. Terminal 5 has a thing called 'conformance' that means that if you have't cleared security (I think its) 35 minutes before boarding they willnot let you through to departures.

So . . . you need to give us more information.

I will be flying on one ticket but 2 different airlines. Flying British Airways to Heathrow, and American Airlines to Dallas. I will have carry on luggage only. I did find another flight that gives me 2 hrs 5 min.

flying on one ticket but 2 different airlines: BA to Heathrow, and American Airlines to Dallas Texas

OK -- totally doable - assuming your BA flight isn't delayed of course - but you do have to switch terminals. (checked luggage would not make a difference one way or the other since they are on the same booking and would be checked through)

You will land at Terminal 5 and depart from Terminal 3. I think 75 minutes is the MCT (minimum legal connection time for domestic BA to International AA). There is an airside bus but from what I read on Flyer Talk many prefer to go landside and take the Elizabeth Line and go through security at T-3.

Are you flying in business or coach? If in Business that will help a lot since you will get off the plane first and will have express security at T-3.