Can someone explain Ephesians 6:5?

If you look at it in the context of the entire chapter you'd realize that Paul was instructing people about authority and how it should be seen ending with the ultimate authority. This is the problem in just looking at one verse of scripture and trying to assign meaning to it. You can't obtain a full understanding without first knowing  the full context in which something was said or written.

It's pretty simple. Paul is telling slaves to be obedient to their owners.

Think of the many slaves in the Roman Empire who accepted Christianity. They were the property of the men who owned them, dependent on them for all life’s provisions.

 Yet they had to exercise their Christian consciences and if their masters should command them to perform acts in violation of Christian principles they would have to refuse, recognizing God and his Son as their superior masters.

 This, would take great faith indeed.

Slaves played a significant part in Roman culture. There were several million of them in the Roman Empire.at this time. Because many slaves and owners had become Christians, the early church had to deal straighforwardly with the question of master/slaves relations. Paul's statement neither condemns nor condones slavery.

IF YOU ARE A SERVANT, SERVE AS THOUGH YOU WERE SERVING MESSIAH.

Deana, slavery as noted in the New Testament biblical passages, has a far different meaning than how mankind enforced slavery.

Listen carefully:
The Apostle Paul described himself as a slave who belonged to Christ; Romans 1:1, Philippians 1:1.
Therefore, exhorted his listeners not to be slaves to sin (see Romans 6:15-23), and encouraged them to be slaves to one another (see Galatians 5:13).

Paul even said that Christ took on the nature of a slave and became poor for our sake; 2 Corinthians 8:9, Philippians 2:7.

His audience knew what it meant to be a slave - not surprising since Christianity’s compassion for the lowly earned it a reputation as a “slave religion.” 

However, this language of Paul does not mean he endorsed slavery or that he thought it should be a part of God’s kingdom.

Furthermore, we come to the deeply troubling history of slavery in the U.S., even of slaveholders who deemed themselves Christians, one cannot appeal to Christianity to justify this ancient and immoral practice.

For a complete understanding, I suggest you carefully review the following web link:
https://www.catholic.com/magazine/online-edition/the-bible-is-not-silent-on-slavery

Simple.  Example.  You slave for your employer.  Eph 6:5 tells you to be a good, honest, hard working employee just as you would do to be a real Christian and not a phony one

What does heeding this counsel require? The Christian should be respectful of his employer, doing what is required of him as if he were in the direct service of God and Christ. He should not loaf, working only when he is under observation. By being industrious, honest and conscientious, the Christian will prevent bringing reproach upon God and Christ. He will be showing that his faith in God has made him a better worker, thereby making true Christianity more attractive to observers.

Sure.

Paul (the author)
is instructing Christian slaves
to be obedient to their masters.

Not without reading all the bit that came before that one verse.  The letter is about how Christians relate to other people (after it's dealt with how they relate to God through Christ.) Chapter 6 deals with children and fathers relating to each other, then it urges Christian slaves to be respectful to their masters (equally if they are not Christian owners). And then it tells Christian masters how to respectfully treat their slaves (whether or not those slaves are Christians.)