It depends on the size of the house. Just doing the sums, there will usually be two people working as a minimum - for practical, safety and efficiency. They will need a van, plus some equipment. Even if they each agree to work for £10/hr (unlikely), include nat.insurance, taxes, holidays etc they have to be charging £40/hr minimum. Including transport to get to the site = 9 +hrs per day. So the min. labour cost is approx £360 / day, plus van costs, + paint & materials, + scaffolding, + liability insurance, + accident insurance, + office/admin costs, + accountant, + etc.
A professional has to provide a good job & result, otherwise clients complain fast. A DIY person accepts the odd splat of paint on the drive! Also painters have to reckon that they will lose days due to weather, somebody has to pay.
Put like that, your quote of £5000 may not be crazy.