There is a rapidly growing number of open-source Large Language Models (LLMs) and benchmark datasets to compare them. While some models dominate these benchmarks, there is typically no single model that achieves the best accuracy in all tasks and use cases. In this work, we address the challenge of selecting the best LLM for new tasks out of a collection of models. We propose a new formulation for the problem, in which benchmark datasets are repurposed to learn a ``router'' model for this LLM selection and show that this problem can be reduced to a collection of binary classification tasks. We demonstrate the utility and limitations of learning model routers from various benchmark datasets, where we consistently improve performance upon using any single model for all tasks.