Question: Auldhame Castle is located half a mile from another castle that is located how far from North Berwick ?

Context paragraphs:
North Berwick Line: The North Berwick Line is a railway line linking Edinburgh with North Berwick in Scotland.  The route follows the East Coast Main Line as far as Drem where it then branches to the north.

Drem railway station: Drem railway station serves the village of Drem in East Lothian, 5 mi from the seaside town of North Berwick in Scotland.  It is located on the East Coast Main Line (ECML) 18 mi east of Edinburgh Waverley.  Passenger services are provided on the Abellio ScotRail North Berwick Line, and the junction where the North Berwick branch diverges from the ECML is a short distance to the east of the station.

North Berwick Golf Club: The North Berwick Golf Club (NBGC), at North Berwick, East Lothian, was founded in 1832.  It is the 13th oldest golf club in the world and only St Andrews hosts a club which has played continuously over the same course for longer.  Although the NBGC was the first club in the world to allow female members, full membership rights were only granted to ladies in 2005.  The club is based at the North Berwick West Links golf course.

North Berwick railway station: North Berwick railway station is a railway station serving the seaside town of North Berwick in East Lothian, Scotland.  It is the terminus of the Edinburgh to North Berwick Line, 22+1/4 mi east of Edinburgh Waverley .

North Berwick Branch: The North Berwick Branch was a short railway branch line built by the North British Railway to connect North Berwick, in East Lothian, Scotland to its main line.  It was built as a tactical means of excluding competitors from the area, and when it opened in 1850 it was loss making.  The later development of North Berwick as a resort and a golfing centre transformed the branch line.

Auldhame Castle: Auldhame Castle is a ruined L-plan tower house standing on a ridge above Seacliff beach, about 3 miles east of North Berwick in East Lothian, and less than half a mile from Tantallon Castle.  The castle was built in the 16th century, probably by Adam Otterburn of Reidhall, Lord Provost of Edinburgh.  It consists of a three-storey main block with a projecting stair-tower.  Part of a vaulted basement remains, but the upper floors are mostly gone.

Noble High School (Maine): Noble High School is a public high school in North Berwick, Maine serving students in grades 8-12 from the towns of Berwick, North Berwick, and Lebanon.  NOBLE is an acronym for the three towns that NHS serves (NOrth Berwick, Berwick, and LEbanon).  Noble High School is a member of the Coalition of Essential Schools.

North Berwick witch trials: The North Berwick witch trials were the trials in 1590 of a number of people from East Lothian, Scotland, accused of witchcraft in the St Andrew's Auld Kirk in North Berwick.  They ran for two years and implicated seventy people.  These included Francis Stewart, 5th Earl of Bothwell on charges of high treason.  The "witches" held their covens on the Auld Kirk Green, part of the modern-day North Berwick Harbour area.  The confessions were extracted by torture in the Old Tolbooth, Edinburgh.  The main source for this story was published in a 1591 pamphlet "Newes from Scotland" and was subsequently published in King James's dissertation on contemporary necromancy titled "Daemonologie" in 1597.

Tantallon Castle: Tantallon Castle is a semi-ruined mid-14th-century fortress, located 5 km east of North Berwick, in East Lothian, Scotland.  It sits atop a promontory opposite the Bass Rock, looking out onto the Firth of Forth.  The last medieval curtain wall castle to be constructed in Scotland, Tantallon comprises a single wall blocking off the headland, with the other three sides naturally protected by sea cliffs.

Aberlady, Gullane and North Berwick Railway: The Aberlady, Gullane and North Berwick Railway was promoted independently to develop settlements between Longniddry and North Berwick in East Lothian, Scotland.  It opened its line from a junction near Longniddry as far as Gullane in 1898, but never succeeded in financial terms, and it never competed its line to North Berwick, which already had a branch railway.

Supporting paragraphs: Auldhame Castle Tantallon Castle
Answer: 5 km