This year (1865) is a difficult one when it comes to find a house displaying 1865 as the year of construction.
So, the only thing I could find are memorials displaying the year 1965. Hereunder are a few examples.
The first one concerns king Leopold II of Belgium. He was born in 1865. The equestrian statue displaying the year is located at the rear of the Royal Palace.
The second one relates to Theordore Verhaegen, the founder of the Université Libre de Bruxelles. The bronx statue was made in 1865 by Guillaume Geefs, a Belgian sculptor. There is anothe statue remembering Joseph Lebeau, a Belgian politician of the early years of Belgian independence. The statue is located in the crossing of the Avenue de Tervuren with the Boulevard de la Woluwe.
Two pictures are about the monument to the Belgian painter Antoine Wiertz in Brussels. He died in 1865. Some of his painting are very especial. I was struck by this one where Napoleon id depicted being consumed by flames in hell. The painting is titled Scene from Hell.
There is also a memorial to Felix Haps, a Brussels benefactor of the catholic charities. The last memorial rememembers Paul Hymans, another Belgian politician who was minister for Foreign Affairs in the years after World War I. Here is a better picture of this memorial: http://www.brusselsremembers.com/memorials/paul-hymans-at-rue-ducale.