Million Invested In Treating Bruising's...
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It is possible. A beech is a low water demand tree, but if your house is founded on a highly shrinkable clay soil 5m is close enough to have an impact on poorly designed foundations. Your foundations should be about 1.5m below ground level to get below the 'zone of influence'. A house built in the last 25 years or so should be ok, but this was often neglected in the past.
However, if it's not a highly shrinkable clay there's nothing to worry about. Contact your local authority and they should be able to put you in contact with a building control officer who should be aware of local soil conditions and advise accordingly.