The 5th César Awards ceremony, presented by the Académie des Arts et Techniques du Cinéma, honoured the best French films of 1979 and took place on 2 February 1980 at the Salle Pleyel in Paris. The ceremony was chaired by Jean Marais and hosted by Pierre Tchernia and Peter Ustinov. Tess won the award for Best Film.

The winners are highlighted in bold:

• Best Film:
  Tess, directed by Roman Polanski
  Womanlight directed by Costa Gavras
  Don Giovanni, directed by Joseph Losey
  I... comme Icare, directed by Henri Verneuil
• Best Foreign Film:
  Manhattan, directed by Woody Allen
  Apocalypse Now, directed by Francis Ford Coppola
  Die Blechtrommel, directed by Volker Schlöndorff
  Hair, directed by Miloš Forman
• Best Actor:
  Claude Brasseur, for The Police War
  Jean Rochefort, for Courage - Let's Run
  Yves Montand, for I... comme Icare
  Patrick Dewaere, for Série noire
• Best Actress:
  Miou-Miou, for La Dérobade
  Romy Schneider, for Womanlight
  Dominique Laffin, for The Crying Woman
  Nastassja Kinski, for Tess
• Best Supporting Actor:
  Jean Bouise, for Coup de tête
  Michel Aumont, for Courage - Let's Run
  Bernard Blier, for Série noire
  Bernard Giraudeau, for Le Toubib
• Best Supporting Actress:
  Nicole Garcia, for Le Cavaleur
  Dominique Lavanant, for Courage - Let's Run
  Maria Schneider, for La Dérobade
  Myriam Boyer, for Série noire
• Best Director:
  Roman Polanski, for Tess
  Costa Gavras, for Womanlight
  Joseph Losey, for Don Giovanni
  Jacques Doillon, for La Drôlesse
• Best Writing:
  Bertrand Blier, for Buffet froid
  Jacques Doillon, for La Drôlesse
  Henri Verneuil, Didier Decoin, for I... comme Icare
  Alain Corneau, Georges Perec, for Série noire
• Best Cinematography:
  Ghislain Cloquet, for Tess
  Jean Penzer, for Buffet froid
  Néstor Almendros, for Perceval le Gallois
  Bruno Nuytten, for Les Soeurs Brontë
• Best Sound:
  Pierre Gamet, for Womanlight
  Alain Lachassagne, for Martin et Léa
  Jean-Pierre Ruh, for Perceval le Gallois
  Pierre Lenoir, for Retour à la bien-aimée
• Best Editing:
  Reginald Beck, for Don Giovanni
  Claudine Merlin, for Buffet froid
  Henri Lanoë, for Le Cavaleur
  Claudine Merlin, for Les Soeurs Brontë
  Thierry Derocles, for Série noire
• Best Music:
  Georges Delerue, for L'Amour en fuite
  Vladimir Cosma, for La Dérobade
  Ennio Morricone, for I... comme Icare
  Philippe Sarde, for Tess
• Best Production Design:
  Alexandre Trauner, for Don Giovanni
  Théobald Meurisse, for Buffet froid
  Jacques Saulnier, for I... comme Icare
  Pierre Guffroy, for Tess
• Best Animated Short:
  Demain la petite fille sera en retard à l'école, directed by Michel Boschet
  Barbe bleue, directed by Olivier Gillon
  Les Troubles fêtes, directed by Bernard Palacios
• Best Fiction Short Film:
  Colloque de chiens, directed by Raúl Ruiz
  Nuit feline, directed by Gérard Marx
  Sibylle, directed by Robert Cappa
• Best Documentary Short Film:
  Petit Pierre, directed by Emmanuel Clot
  Georges Demeny, directed by Joël Farges
  Panoplie, directed by Philippe Gaucherand
  Le Sculpteur parfait, directed by Rafi Toumayan
• Honorary César:
  Pierre Braunberger
  Louis de Funès
  Kirk Douglas

• 52nd Academy Awards
• 33rd British Academy Film Awards

• Official website
• 5th César Awards at IMDb
• 5th César Awards at AlloCiné