Fear
can mean a loving reverence or a real terror. The context of the passage gives some clues to the correct interpretation. Previously the word was used with regards to reverence (Ephesians 5:21, Ephesians 5:33), which is the same meaning that it has in this sentence.1 Trembling
is a word used to denote a fear that is so great it cannot be concealed.2 Where fear and trembling are used together elsewhere in the New Testament (Philippians 2:12; 1 Corinthians 2:3) they denote a loyalty whose nervousness lies in the thought that a loved one might be let down.3
Paul is not encouraging slaves to melt in fear before their earthly master, but to conduct themselves in a manner that will make it clear to their master that they respect him and seek to obey him.
5 Bondservants, obey your earthly masters with fear and trembling, with a sincere heart, as you would Christ,