Wyner and Ziv  determined the rate-distortion function of source coding with side information. In this paper, we consider a network extension of their scenario: Many sources have to be compressed in a rate-distortion sense for a decoder that has access to uncompressed side information about the sources. This may model a sensor or multi-camera network situation where the data collection point itself also has a sensor/camera attached to it. Basic results for the case of two sources and side information have been presented recently , . The present paper extends these results to the case of more than two sources. In particular, we derive an achievable rate-distortion region, and an outer bound to the best rate-distortion region. These two do not coincide in general, but they do in the special case where the sources are conditionally independent given the side information. We illustrate this result with applications. For example, we discuss two different kinds of rate losses of distributed compression as compared to joint (i.e., centralized) compression. Thereafter, we show that in some cases, our result permits to derive bounds to the rate-distortion region for the distributed compression problem without side information, and we also show how a certain source-channel separation theorem can be established.