Signs like this are an artefact of earlier postcode assignment schemes that recall when the sign was manufactured. They may or may not sync up with the current postcode, or may indicate only a portion of the current postcode. There is no effort I'm aware of to make the older signs to synch up (presumably because of the cost). The discrepancies are not, to my knowledge, a source of public anxiety.
What is the purpose of the Number 5? It refers to the first postal code for Bailey Wells Avenue under the current scheme, the first postal code was BD5 (Bradford). The current postal code for Bailey Wells Avenue is BD5 9EA.
The upside down sign above it is a curious relic. It looks like the sign started out as 'Morley Carr' and then was reused as 'Earl Street'. I can only guess that the house owner purchased the sign as scrap and used it to cover some damage to the building. Morley Carr is a long ways away near Middlesbrough and Earl Street is newer.
Postcodes have evolved since the original Postal Act in the 19th century, and the latest reform was a project spanning 14 years.
The current numbering scheme is administered by the Office of National Statistics, but street signs are most often installed by the local authority under the overall supervision of Parliament. National signs are installed by the Ministry of Transport (which reports in to the Home Office).
Adding: these artefacts are of marginal value to the traveller because they may indicate the relative age of the neighbourhood, but again some historic districts have new signs. Also, the police, fire brigade, and emergency services use SATNAV and rarely (if ever) refer to the street sign.
Related article: In 1965 British Roads Got Their Identity