In Act 5 Scene 1 , is Portia really angry with Bassanio when she finds that he had given away his ring?

While I agree with the first answer that Shakespeare does not characterize Portia as angry with Bassanio's giving away her ring, I do think that the scene (and the whole ring plot for that matter) has more significance than simply serving as comic relief after Act 4's intense trial.  Admittedly, it is humorous that Bassanio gives away his wife's ring without even knowing that he is bestowing it upon his wife, but Shakespeare also uses the ring plot to demonstrate what he perceives as a weakness in men. Throughout the play, Shakespeare portrays Portia as wise--wiser than any of the male characters in Merchant--and seems to imply that men are easily fooled and manipulated by women.  Portia promotes this view when she explains toNerissa what she plans to do in Venice by being disguised as a man; Portia harps on male weaknesses and what she views as their foolishness. Similarly, Portia sets up the ring plot to "test" her husband, and surely enough he fails the test.  When she gives the ring back, she does not do so with anger, but she does demonstrate a patronizing, superior attitude; it is as if she is chiding a younger person for his foolishness.  Realistically, most men would not appreciate their wives manipulating them in such a manner.

As to why Shakespeare characterizes Portia in this manner, we most likely will never know--it could have been to praise the independent Elizabeth who reigned during part of Shakespeare's career, or it could have been a warning to fellow men to be wary of intelligent, take-charge women.