1. 事实胜于雄辩。 (Shìshí shèng yú xióngbiàn)

— Facts beat eloquence.

From Lu Xun's "Hot Wind" (鲁迅《热风题记》), it's like, "Actions speak louder than words."

2. 一言既出，驷马难追。(Yìyán jì chū, sìmǎ nán zhuī / 'a word already produced, team-of-4-horses difficult chase')

— A team of horses will struggle to chase down a spoken word.

From "The Analects of Yan Yuan" (《论语·颜渊》), it means a word spoken can never be taken back, or a promise must be kept.

3. 路遥知马力，日久见人心。(Lùyáo zhī mǎlì, rìjiǔ jiàn rénxīn / 'road distant know horse strength, days old see man heart')

— As distance tests a horse's strength, time reveals a person's character.

From the anonymous work "Fight Gratitude" (《争报恩》) of the Yuan Dynasty (1279–1368), when Mongol horsemen ruled China, this saying tells us that a long period of testing is needed to understand someone's nature and capabilities.

4. 无规矩不成方圆。(Wú guīju bù chéng fāngyuán / 'no standards not become perimeter')

— Without standards, no boundaries are set.

From the works of Mencius and his students (《孟子·离娄上》), it means: nothing can be accomplished without norms or standards; or: without rules, we're nothing but savages.

5. 惩前毖后。 (Chéngqiánbìhòu / 'punish before prevent after')

— Punishing those who come before stops those who come after from doing something.

From "Sacrificial Odes of Zhou" (《周颂》) in the Confucian classic "Book of Songs" (《诗经》), it means: to criticize former mistakes firmly to prevent them happening again; or: learn from past mistakes to avoid future ones.