I was wondering buy this ASIC miner of 5GH/s to mine Litecoin.
I want know, can I mine Litecoin with this powerful tool? If not, there any ASIC miner's that can mine Litecoin?
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Litecoin uses a different proof of work than Bitcoin, so that hardware won't be compatible(it won't be solving the right problems).
One of the motivations of Litecoin was to make CPU mining viable by making it difficult to create efficient GPU/FPGA/ASIC miners, so it's unlikely that you can find specialized hardware for this purpose. I think that some GPUs do give a speedup over CPU mining with Litecoin, but it isn't as dramatic as with Bitcoin.
No, you can't mine Litecoin with any of Butterfly Labs' products. There is an ASIC miner in development by Alpha Tech http://alpha-t.net/ that they claim will be able to.