I read the other two responses and they are good but I want to make it more clear to you how the two phrases can mean very different things. If someone says "She has played piano since 2005" that can only mean that she started taking lessons and has played regularly since then. If someone says "She has been playing piano since 2005" because of the context you know that it means the same thing as the above sentence, BUT it could also mean that she has been playing piano continuously since 2005. This sets up a good English joke actually... If someone were to say "I have been playing piano since 2005" you could say "Wow, your hands must be tired!" Maybe nobody will laugh but at least you showed how well you understand English.

You can never use past continuous (e.g. "was playing") or past simple (e.g. "played") before "since". You chose the two correct tenses. In this example, the meanings are very close and almost interchangeable. "has played" emphasises the result or achievement (e.g. What has he done in his life since....?). "has been playing" emphasises the activity (e.g. What has she been doing since....?).

FAIR WARNING: I am NOT an English teacher, but I can give you the perspective of a native English speaker. To my ears it is perfectly normally to say either of these: a) She has been playing piano since she was 4 years old. / She has been playing piano since 1990. b) She has played piano since she was 4. / She has played piano since 1990. In [a] we are emphasizing the duration of time that whoever "she" is has been playing and the fact that the action is ongoing and influences the present. In [b] it's actually very close maybe just a little less direct emphasis on the duration of time the action has been occurring for and more emphasis on the outcome. Some potential contexts: Mary is an accomplished pianist. She has been playing the piano since she was four years old and now she plays with the New York Philharmonic. Mary always dreamed of playing the piano for huge crowds of people. She has played the piano since she was four and graduated with a degree in piano performance from Julliard in 2007.