Wow...so hard to limit oneself to five only. Ang Lee has to be there, of course, for Brokeback Mountain, which remains the single most important film I have yet experienced. I selected Alfred Hitchcock for his technical brilliance, historical importance, and enduring poetic resonance (Jean-Luc Godard has written most persuasively of Hitchcock being a rare poet of cinema). Stanley Kubrick made the cut for his exceptional intelligence and visionary sensibility--world cinema lost so much with his death in 1999. Robert Altman is included because he remains one of the most consistently adventurous filmmakers around--his 1970 Brewster McCloud is a personal favorite of mine. Lastly, Elia Kazan got in due to his impeccably sensitive skill as a director of actors; a 1961 classic like Splendor in the Grass represents classic Hollywood filmmaking at its finest, an exemplar of what that industry could produce when inspiration and technical finesse came together so neatly.
Lots of important filmmakers I could recommend for a more inclusive list; in no particular order:
Charles Chaplin--remains the single most important figure in cinematic history. A frequently brilliant and always graceful actor, and a director with a clear visual sensibility of understated elegance, and a high degree of moral engagement.
Lois Weber--one of the earliest female filmmakers, Weber was a master of mise-en-scene, as evidenced by her 1915 masterpiece Hypocrites. This film shows her fully worthy of other pioneers of film art like D.W. Griffith and Victor Sjostrom.
Louis Feuillade--French specialist in thrilling serials during the 1910s. Like Weber, Feuillade achieved early mastery of beautiful mise-en-scene, exhibiting particular flair for staging in depth. Works like the marvellous 1915-16 Les Vampires and the lesser but still rewarding 1916-17 Judex are rife with mystery, elegance, and an uncanny mixture of the sinister and the zany. These serials were highly prized by the Surrealists, whose concerns and strategies they in some ways intimate.
Yasujiro Ozu--beloved Japanese master of the domestic drama (and domestic comedy). Ozu is one of the greatest of all filmmakers, though his movies were slow to make inroads among audiences outside of Japan. My personal favorite of his films is probably also his masterpiece, the 1932 late silent feature I Was Born, But....
Jean Renoir--not one of my favorite film directors, but nonetheless an artist of the first rank, and from all accounts a man of great heart and beautiful spirit. His 1937 La Grande illusion and 1939 La Regle du jeu are justifiably celebrated as classics of world cinema, though neither is a personal favorite of mine.
Michelangelo Antonioni--one of the greatest of Italian film directors. His 1962 masterpiece L'eclisse and the somewhat lesser though still profound 1964 Il deserto rosso remain as haunting and pertinent today as when they first graced art-house screens some four decades ago.
Robert Bresson--austere, deeply contemplative French director of the first rank. Bresson's aesthetic is one of uncompromising rigor, and his moral gaze is ruthless and searing, all combining to make him one of the most important artists to have worked in the medium of film. My personal favorite of his movies, the 1966 masterpiece Au hasard Balthazar, ranks with Brokeback Mountain both in having one of the most devastating endings in cinema and in being one of the most important films ever made.
D.W. Griffith--highly controversial director of vital historical importance. His 1915 The Birth of a Nation, frequently vile and enthralling in equal measure, is arguably the single most influential work in film history. His 1916 Intolerance is fully its equal in technical brilliance while being considerably more humane and warm in its moral vision.
Satyajit Ray--legendary Indian filmmaker who was a real Renaissance man, being equally gifted as draughtsman, graphic artist, and musician/composer. Ray was a pioneer in carving a niche for artistic, personal cinema within the Indian film industry, and he achieved cinematic greatness with his very first film, the 1955 masterpiece Pather Panchali.
Orson Welles--one of the rare figures in film history truly worthy of the epithet of genius. His 1941 debut feature Citizen Kane remains his most celebrated work, but I prefer the quieter, more mature masterpiece that is the 1942 The Magnificent Ambersons, not to mention the scintillating yet gritty 1958 noir classic Touch of Evil, in addition to the frequently exhilarating, perplexing 1974 F for Fake, probably Welles's most personal movie. Welles was a brilliant, exceptionally insightful human being whose vast film legacy is still in the process of being recovered and reevaluated.
Cheers,
Scott