Mily Balakirev César Cui Modest Mussorgsky Nikolay Rimsky-Korsakov Aleksandr Borodin The Five refers to a circle of composers, also known as The Mighty Handful, who met in St. Petersburg, Russia, in the years 1856-1870: Mily Balakirev (the leader), César Cui, Modest Mussorgsky, Nikolai Rimsky-Korsakov, and Alexander Borodin. The group had the aim of producing a specifically Russian kind of art music, rather than one that imitated older European music or relied on European-style conservatory training. In a sense, they were a branch of the Romantic Nationalism movement in Russia, with the Abramtsevo Colony and Russian Revival striving to achieve similar goals in the sphere of fine arts.

Name
Aleksandr Borodin (1833 – 1887)
César Cui (1835 – 1918)
Modest Mussorgsky (1839 – 1881)
Nikolai Rimsky-Korsakov (1844 – 1908)
The formation of the group began in 1856, with the first meeting of Balakirev and César Cui. Modest Mussorgsky joined them in 1857, Nikolai Rimsky-Korsakov in 1861, and Alexander Borodin in 1862. Before them, Mikhail Glinka and Alexander Dargomyzhsky had gone some way towards producing a distinctly Russian kind of music, writing operas on Russian subjects, but The Mighty Handful represented the first concentrated attempt to develop such a music, with Stasov as their artistic advisor and Dargomyzhsky as an elder statesman to the group, so to speak.
The circle began to fall apart during the 1870s, no doubt partially due to the fact that Balakirev withdrew from musical life early in the decade for a period of time. All of "The Five" are buried in Tikhvin Cemetery in St. Petersburg.

History
Rimsky-Korsakov provides the following picture of "The Mighty Handful" in his memoirs, Chronicle of My Musical Life (translated by J. A. Joffe):
On their tastes
"The tastes of the circle leaned towards Glinka, Schumann, and Beethoven's last quartets ... they had little respect for Mendelssohn ... Mozart and Haydn were considered out of date and naive ... J. S. Bach was held to be petrified ... Chopin was likened by Balakirev to a nervous society lady ... Berlioz was highly esteemed ...Liszt was comparatively unknown ... Little was said of Wagner ... They respected Dargomyzhsky for the recitative portions of Rusalka ... [but] he was not credited with any considerable talent and was treated with a shade of derision. ...Rubinstein had a reputation as a pianist, but was thought to have neither talent nor taste as a composer."
On Balakirev
"Balakirev, who had never had any systematic course in harmony and counterpoint and had not even superficially applied himself to them, evidently thought such studies quite unnecessary ... An excellent pianist, a superior sight reader of music, a splendid improviser, endowed by nature with the sense of correct harmony and part-writing, he possessed a technique partly native and partly acquired through a vast musical erudition, with the help of an extraordinary memory, keen and retentive, which means so much in steering a critical course in musical literature ... He instantly felt every technical imperfection or error, he grasped a defect in form at once. Whenever I or other young men, later on, played him our essays at composition, he instantly caught all the defects of form, modulation, and so on, and forthwith seating himself at the piano, he would improvise and show how the composition in question should be changed exactly as he indicated, and frequently entire passages in other people's compositions became his and not their putative authors' at all. He was obeyed absolutely, for the spell of his personality was tremendous. ... His influence over those around him was boundless, and resembled some magnetic or mesmeric force. ... he despotically demanded that the tastes of his pupils should exactly coincide with his own. The slightest deviation from his taste was severely censured by him. By means of raillery, a parody or caricature played by him, whatever did not suit him at the moment was belittled — and the pupil blushed with shame for his expressed opinion and recanted...."
On their abilities
"Balakirev considered me a symphony specialist ... in the sixties, Balakirev and Cui, though very intimate with Mussorgsky and sincerely fond of him, treated him like a lesser light, and of little promise at that, in spite of his undoubted talent. It seemed to them that there was something missing in him and, in their eyes, he was in need of advice and criticism. Balakirev often said that Mussorgsky had "no head" or that his "brains were weak." ... Balakirev thought that Cui understood little in symphony and musical forms and nothing in orchestration, but was a past master in vocal and operatic music; Cui, in turn, thought Balakirev a master in symphony, form, and orchestration, but with little liking for operatic composition and vocal music in general. Thus they complemented each other, but each, in his own way, felt mature and grown up. Borodin, Mussorgsky, and I, however—we were immature and juvenile. Obviously, towards Balakirev and Cui we were in somewhat subordinate relations; their opinions were listened to unconditionally ..."

Timeline