There are those who believe that 1 Corinthians 5:8 teaches we are to celebrate the Passove (or the Feast of Unleavened Bread), and so teaches we are to follow the Mosaic (festival) Law.
1 Corinthians 5:8 does not teach to celebrate Passover or the Feast of Unleavened Bread (while I do not see Scripture saying Christians must celebrate them, I certainly see nothing wrong with celebrating them). We have to look at the passage in context.
5 I have decided to deliver such a one to Satan for the destruction of his flesh, so that his spirit may be saved in the day of the Lord Jesus. 6 Your boasting is not good. Do you not know that a little leaven leavens the whole lump of dough? 7 Clean out the old leaven so that you may be a new lump, just as you are in fact unleavened. For Christ our Passover also has been sacrificed. 8 Therefore let us celebrate the feast, not with old leaven, nor with the leaven of malice and wickedness, but with the unleavened bread of sincerity and truth.
9 I wrote you in my letter not to associate with immoral people ; 10 I did not at all mean with the immoral people of this world, or with the covetous and swindlers, or with idolaters, for then you would have to go out of the world. 11 But actually, I wrote to you not to associate with any so-called brother if he is an immoral person, or covetous, or an idolater, or a reviler, or a drunkard, or a swindler -not even to eat with such a one. 12 For what have I to do with judging outsiders ? Do you not judge those who are within the church? 13 But those who are outside, God judges. REMOVE THE WICKED MAN FROM AMONG YOURSELVES .
This passage is a word picture about removing the sinner from the midst of the congregation. In verse 5, we see Paul has decided to hand over the man who had relations with his father’s wife to Satan. Verse 7 tells us to clean out the leaven from within our church (which is seen more clearly in verses 9-13). Verse 8 tells us the leaven is malice and wickedness, and unleavened bread is sincerity and truth. We are to be unleavened bread and clean out the leaven from among us – remove the wicked from among the Church.
CHRIST is the Passover. We celebrate HIM and what He has done for us - every day. In essence, we are to celebrate the Feast of Unleavened Bread daily – living a life without leaven, or without malice and wickedness.
So no, this passage does not teach to follow the Mosaic Law. We are free to celebrate the festivals if we so desire, so remind us of what God has done for us and honor God. But this is not a requirement for believers in Christ – we have been freed from the Law.

