.NET Fiddle

CSharp · Console

/Program.cs

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

public class Program
{
	

	
	public static void Main()
	{
		
		var things = GetThings();
		
		//The original S/O answer
		var stackFlowAnswer = things
                    .Select(p => new { ThingId = p.ID, Age = DateTime.Now.Year - p.YearBuilt })
                    .GroupBy(p => p.Age > 65 ? 5 : (int)((p.Age - 16) / 10))
                    .Select(g => new { 
                        AgeGroup = g.Key == 5 ? "> 65" : string.Format("{0} - {1}", 
                        g.Key * 10 + 16, 
                        g.Key * 10 + 25), 
                        Count = g.Count() });
		
		//my attempt to increase the numbner of bucets and start from zero.
		var thingsByAge = things
                    .Select(p => new { ThingId = p.ID, Age = DateTime.Now.Year - p.YearBuilt })
                    .GroupBy(p => p.Age > 40 ? 8 : (int)((p.Age + 1) / 5))
                    .Select(g => new { 
                        AgeGroup = g.Key == 8 ? "> 40" : string.Format("{0} - {1}",  //"g.Key == 7" puts that group at index 7 (the last one)
                        g.Key,
                        g.Key * 5 + 4,
                        g.Key * 5 + 9,
                        g.Key * 5 + 14,
                        g.Key * 5 + 19,
                        g.Key * 5 + 24,
                        g.Key * 5 + 29,
                        g.Key * 5 + 34,
                        g.Key * 5 + 39), 
                        Count = g.Count() }
                    );
		
		var json = Newtonsoft.Json.JsonConvert.SerializeObject(thingsByAge, Newtonsoft.Json.Formatting.Indented);
		//var json = Newtonsoft.Json.JsonConvert.SerializeObject(stackFlowAnswer, Newtonsoft.Json.Formatting.Indented);
		Console.WriteLine(json);
		
	}
	
	public static List<Thing> GetThings()
	{
		 var things = new List<Thing>();
			things.AddRange(MakeThings(2, 2019)); things.AddRange(MakeThings(12, 2018)); things.AddRange(MakeThings(2, 2017)); things.AddRange(MakeThings(0, 2016)); things.AddRange(MakeThings(0, 2016));
			things.AddRange(MakeThings(7, 2015)); things.AddRange(MakeThings(8, 2014)); things.AddRange(MakeThings(15, 2013)); things.AddRange(MakeThings(5, 2012)); things.AddRange(MakeThings(5, 2011));
			things.AddRange(MakeThings(0, 2010)); things.AddRange(MakeThings(0, 2009)); things.AddRange(MakeThings(0, 2008)); things.AddRange(MakeThings(0, 2007)); things.AddRange(MakeThings(0, 2006));
			things.AddRange(MakeThings(9, 2005)); things.AddRange(MakeThings(4, 2004)); things.AddRange(MakeThings(5, 2003)); things.AddRange(MakeThings(5, 2002)); things.AddRange(MakeThings(5, 2001));
			things.AddRange(MakeThings(1, 2000)); things.AddRange(MakeThings(5, 1999)); things.AddRange(MakeThings(5, 1998)); things.AddRange(MakeThings(5, 1997)); things.AddRange(MakeThings(5, 1996));
			things.AddRange(MakeThings(1, 1995));
			things.AddRange(MakeThings(1, 1990));
			things.AddRange(MakeThings(1, 1985));
			things.AddRange(MakeThings(1, 1980));
			things.AddRange(MakeThings(1, 1975));
			things.AddRange(MakeThings(1, 1970));
			things.AddRange(MakeThings(1, 1965));
			things.AddRange(MakeThings(1, 1960));
			things.AddRange(MakeThings(1, 1955));
			things.AddRange(MakeThings(1, 1950));
			things.AddRange(MakeThings(1, 1945));
		
		return things;
	}
	
	public static List<Thing> MakeThings(int count, int year)
	{
		var ret = new List<Thing>();
		for(var i = 0; i < count; i++)
		{
			ret.Add(new Thing(year));
		}
		return ret;
	}
	
	public class Thing
	{
		public Thing(int yearBuilt)
		{
			this.ID = Guid.NewGuid().ToString();
			this.YearBuilt = yearBuilt;
		}
		public string ID { get; set; }
		public int YearBuilt { get; set; }
		
	}
	
}