The word translated as “You are proud!” is the participle πεφυσιωμένοι, conjugated from the lemma φυσιόω. The King James Version translates it as “And ye are puffed up,” which is a decent translation. The derivative of the Greek stem φυσ- is later found in such English words as emphysema, a disease of the lungs. Notably, the lemma φυσιόω occurs 7 times in 7 verses in the Textus Receptus, and of those 7 occurrences, 6 of them are in the First Epistle to the Corinthians. In other words, the Corinthians had a significant problem being “puffed up”—proud—perhaps moreso than any other Christian church at that time!
Both BDAG1 and Thayer (translating Wilke)2 concur that φυσιόω can be understood as “to make proud” (active voice) or “to be proud” (passive voice). With respect to the Corinthians, it’s possible that there pride was a result of their intellectual knowledge.3
As far as 1 Cor. 5:2 is concerned, Henry Alford (among others) did not believe that the Corinthians were actually proud because of the fornication. He commented that the pride was cum hoc, not propter hoc.4 The Corinthians were proud for other reasons,5 but due to the severity of the sin in 1 Cor. 5:2, the apostle Paul took that moment to express astonishment (and perhaps disgust) that the Corinthians could even dare exhibit pride at all!
References
Alford, Henry. The Greek Testament. Vol. 2. Boston: Lee, 1878.
Arndt, William; Bauer, Walter; Danker, Frederick William. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: U of Chicago P, 2000.
Wilke, Christian Gottlob. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Trans. Thayer, Joseph Henry. Ed. Grimm, Carl Ludwig Wilibald. Rev. ed. New York: American Book, 1889.
Footnotes
1 p. 1069
2 p. 660
3 1 Cor. 8:1: «ἡ γνῶσις φυσιοῖ»—“Knowledge makes proud.”
4 Commentary on 1 Cor. 5:2 (p. 505). Cum hoc (lit. “with this”) is when something occurs with something else. Propter hoc (lit. “because of this”) is when something occurs because of something else. Both are related to a fallacy known as Cum hoc ergo propter hoc.
5 cp. 1 Cor. 4:6, 4:18–19