1 Cor 5: 6-8
"Your boasting is not good. Don’t you know that a little yeast leavens the whole batch of dough? Get rid of the old yeast, so that you may be a new unleavened batch—as you really are. For Christ, our Passover lamb, has been sacrificed. Therefore let us keep the Festival, not with the old bread leavened with malice and wickedness, but with the unleavened bread of sincerity and truth."
First of all, I have never condemned anyone for observing the feast days. I have said that those who find it to be useful for them in their walk with Christ are free to do so, unless they condemn others for not participating in these festivals.
But the point Paul is making in 1. Cor 5, is that we should not be legalistic. Also it states in Hebrews that the old covenant will soon fall away. As if it has been a process since the death of Christ. I understand that Paul would still observe many of these feast days, it is not a sin, and to him it was conveniant for the time, but it is neither a command he gives here.
Hebrews 8:13 ►
"By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will SOON disappear."
Also Hebrews 12:26-27
"At that time his voice shook the earth, but now he has promised, “Once more I will shake not only the earth but also the heavens.” The words “once more” indicate the removing of what can be shaken—that is, created things—so that what cannot be shaken may remain."
Other areas in which we see Paul teaching or practicing for the time being contrary to what he states elsewhere concerning the old covenant, is in his teachings on women to be subordinent to men, and not to teach in church, but to be silent.
Yet it clearly contradicts Galatians 3:26-29, which ask us to look beyond these external, legalistic factors like race, nation, gender, status, genes etc, and look at the inner values and beliefs. Even Christ uttered this in John 7:24:
"Stop judging by mere appearances, but instead judge correctly.”
Matthew 12:37: "For by thy words thou shalt be justified, and by thy words thou shalt be condemned."
So we see how he practice the law of the letter when it was more convenient to do so. According to the culture back then, it was very different from western society today. So he seems to have reasoned according to the spirit even if it seems to be of the letter. Because at that time it was the most reasonable practice.