We are flying from Seattle to Heathrow on Delta and arrive at 3:05 pm (terminal 3). We have a separate ticket booked on British Airways to Edinburgh that departs at 5:25 pm (terminal 5). Will it be possible to go through customs and security and make this flight? If we switch to the 6:30 pm flight will we then have enough time, or do we need to change to the 8 pm? We are not planning to check bags.
It's certainly possible that you could make the flight. You will arrive at terminal 3, follow flight connections and take the bus to terminal 5. Providing you arrive on time this would not be a problem for a 2:20 connection. If you arrive late and miss your connection, you will have to purchase a new ticket. I would recommend you view the history of DL36 SEA-LHR on flightstats to decide if you wish to take that risk.
If you do miss it, there's a good chance you could purchase a new flight with Avios even after arrival, providing you have some Avios from previous crediting to BA, or if you choose to purchase some. An Avios ticket from LHR to EDI would be 4500 avios and £17.50 each way.
Taking a quick look on flightstats, shows it arrived 82 minutes late two days ago. However it generally has a fairly good on-time performance.
Edit: Heathrow suggests the connection typically requires 90 minutes from landing.
BA recently introduced some new ticket types. Previously only expensive flexible and semi-flexible tickets were changeable, but now there are Basic, Plus and Plus Flex tickets. On domestic flights there is business UK. Business UK, Plus and Plus flex tickets allow change of flight on same day if seats in cabin are available. Details here.
As an example for a random date I pulled up:
The difference in price (each way) between basic and plus can be quite minimal. If you chose the latest flight on the day, which is the cheapest, and you chose the Plus fare, you could change it to any earlier flight after you arrive.
Details of plus fare:
If your incoming flight is on time, it is certainly possible to be at the departure gate for EDI by 4:05. Just follow the signs for Connecting Flights and specifically UK Connections.
However, if you are delayed, BA has no real obligation to honor the outbound ticket. They might, depending on circumstances. BA will only protect you, meaning re accommodate at no charge, if you arrive on a delayed BA or other OneWorld flight, even if it's technically a separate ticket. (Note, I know this is an AA rule, presumable BA has the same.)
If not worrying is important to you, take the 2000 flight. T5 departures is not the worst place to wait.