I can give you some transport suggestions. Buy Oyster cards at Heathrow and load each of them with about £20. Use them to get to Marble Arch on the Tube and for any other rides you take on day 1.
Buy one-day National Rail paper travelcards at any mainline train station to use on day 2. They will be good on the Tube, Docklands Light Railway, and National Rail trains within the zones covered and on the entire London bus system. They will qualify you for the 2for1 offers found at www.daysoutguide.co.uk. Those offers include Wimbledon, Lord's Stadium, and Thames River cruises. Print the vouchers you need and take them with you. You won't need your Oyster cards on day 2.
On day 3 use your Oyster cards to travel by Tube or bus to and from a train station from which you will depart for the day trip of your choice. Buy train tickets at the station.
On day 4 buy one-day National Rail paper travelcards again if you're going to visit any places that are on the 2for1 list. Otherwise just use your Oyster cards.
On day 5 use your Oyster cards for any rides you take in the morning and for the Tube to Heathrow.
The Oyster computer will automatically give you the best fare for each ride you take. On any given day you will never pay more than 50 pence less than what a one-day travelcard would cost for the zones in which you travel that day. If you run low, you can top up the card. If you have money left over, you can get a refund at Heathrow, including your deposit.