It is quite common to hear 1 Corinthians 5:6-8 cited in discussions about communion bread. Many sincere Christians think eucharistic bread must be unleavened, and they will sometimes use these verses to prove it. But this is a mistake, both because the position is wrong--Scripture does not require the bread used for the holy Supper to be unleavened--and because the prooftext is invalid. A person may prefer that unleavened bread be used in communion, but this passage has nothing to say about it.
There is no doubt Jesus used unleavened bread when instituting the Lord’s Supper since he did so during the Passover feast and all leavened bread would have been removed from the house. But the Greek language distinguishes common (leavened) bread (ἄρτος) from unleavened [bread] (ἄζυμος), and all of the passages describing or directing observance of the Supper use the word for ordinary (leavened) bread. The Church used leavened bread throughout her early history, but after a Roman bishop introduced the use of unleavened bread, the question of which kind of bread to use became a point of controversy which continues to divide the Roman Catholic and Eastern Orthodox communions to this day.
The Reformed have traditionally treated the kind of bread as a matter of indifference:
“ … whether the bread is to be leavened or unleavened, and the wine to be red or white, is of no consequence. These things are indifferent, and left free to the Church….” --Calvin, Institutes IV.17.43
“As the Lord’s Supper was originally instituted in connection with the Passover, there is no doubt that unleavened bread was used on that occasion. It is evident, however, from the apostolic history, that the Apostles used whatever kind of bread was at hand. There is no significancy either in the kind of bread or in the form of the loaf. It is enough that it is bread. This makes it the proper emblem of Him who declared Himself to be the true bread which came down from heaven.” --Charles Hodge, Systematic Theology III.615
If anything, Reformed Christians seem to have generally preferred the use of leavened bread in communion which would be broken and distributed to the congregation as a symbol of the unity of the Body of Christ.
“We do not deny that the use of fermented bread seems to us the more suitable, both because it is more in accordance with the design of Christ (which was to use common and ordinary bread, which is everywhere to be found); and because it is more appropriate to sustain the sacramental analogy (which consists in signifying our communion with Christ by the similitude of bodily nourishment); and because the necessity of unleavened bread belongs to Jewish ceremonies (which are abrogated and cannot be retained without a certain affectation [kakozelia] of Judaism); and because in the whole ancient church no traces appear of the common use of unleavened bread in the Eucharist before the ninth or tenth century…. The example of Christ neither can nor ought to be made an objection here, because as we have said there was a peculiar reason which impelled him to the use of unleavened bread (which no longer exists). Therefore, his example binds us as to the essence of the thing itself, that we should do whatever he did (take, bless, and break the bread and other acts of this kind mentioned by the sacred writers); but not forthwith as to the particular circumstances, which do not belong to the thing.” --Turretin, Institutes III.430
The historic practice of the Church and the specific language of the NT favor the use of leavened bread. So too does the symbolism explained in 1 Corinthians 10:17: For we, though many, are one bread and one body; for we all partake of that one bread.[1] But unleavened bread is acceptable since nothing requires the presence of leaven in communion.[2] There are many symbolic rationales that can be given for one or the other type of bread, but neither can be required from the text of Scripture. So if you are tempted to use 1 Corinthians 5:6-8 to prove why churches must use unleavened communion bread… don’t. --JME
[1] It is theoretically possible for a congregation to partake of one unleavened piece of bread, but in most cases it will be impracticable.
[2] A comparison between modes of baptism is appropriate. A symbolic rationale can be offered for sprinkling, pouring, or immersion, but Scripture does not require any particular one of these three.