You need to raise a dispute with whoever holds the deposit. What does the check out inventory say needed to be cleaned, redecorated, and done in the garden? What does the check in inventory say about the state of the property? Without knowing that, no one can really answer whether the charges are reasonable for what needed doing nor whether they are reasonable things to claim for. It sounds like they are being CFs but...
Cleaning - the property needs to be at the same level of cleanliness as it was at the start of the tenancy when you leave. You don't have to pay for it to be professionally cleaned but it must be cleaned to the same standard as it was when you moved in.
Gardening - the garden should be in a similar standard condition to how it was when you moved in. You can't be held responsible for plants dying, trimming tall hedges/trees but things you might be charged for could be an unmown lawn, weeds or bare patches in the lawn, weeding, pruning small shrubs/hedges/climbers/ivy if they haven't been kept regularly pruned (assuming they were when you moved in). TBH, in 3 weeks the lawn could well need mowing and although they might be small, the weeds could have grown back. If you let a 5 foot hedge grow to 10 feet and only trimmed stray twigs to neaten it up before you left, that might be a reasonable claim.
Decorating - it is unlikely that they can charge you for decorating after 5 years wear and tear but it depends if there was damage due to negligence or you had done things in breach of contract eg multiple broken tiles, dog-chewed skirting board, mould or water damage, your teenager painted the walls and ceiling of their bedroom black, you painted a stone fireplace or wooden banisters that now need stripping.
Carpet - the deposit schemes look at the quality of the carpet and the age (the landlord will need to provide proof). Good quality carpet is expected to last 20 years, cheap carpet just 5 years. FWIW, IME it is usually new carpets that shed, not old carpets. What does the check-in inventory say about the state of the carpet?