Well, 4-5 hours are really short. I was there last february for an entire day (landed 0730, left 1910) and I just basically walked along the Thamse. The weather was really good and I had a great time, although my feet started to hurt after many hours of walking. I went from LHR into the city with the Picadilly (sp?) Line and got of at the buckingham palace (I forgot the name of the station but you'll be able to find that out) and then started my walk alongside the palace and down to the river. If you have less time, I can definatly recommend taking the bus. There are some very interesting routes. I would recommend buying a city-map. If you do chose to go by bus, which I did later in the day and I was able to see a lot, you should buy a day ticket at the airport. As far as I remember it was about 9 Pounds which is a lot cheaper than buying a ticket for every direction.
So I would recommend you taking the bus as you will be able to see a lot of the city in little time. With a little bit of luck you might even be able to hop onto one of the old, classical busses. I think they only go on one route though...
If you have any other, more specific questions I'd be happy to help out. If you understand German, I can send you a trip report I wrote back then where you might find some additional information.
Enjoy London, it is a fun city! However take enough time to get back to the airport. The city is very full and it could be risky not to have enough time.
Best wishes
Jakob
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