亚马逊客户投诉商品有破损（5个多月前买的），该怎么回应？

你就引用亚马逊的商品退换货政策，然后建议他跟厂商联系，看下能不能退换。
如果是通过UPS、Fed Ex寄件的，跟他说超过90天，就不能要求损坏赔偿了
他可能会申请az，但你肯定赢

购买的30天内买家可以要求退货退款，90天内可以留评或提交claim。如果产品有保修，可以教他怎么跟厂商联系，让厂商帮忙修理或直接退换
他提交的claim会被否决，不会对你的ODR有影响（显示的是订单时间，而不是提交claim的时间）。就算他赢了，亚马逊会出钱赔偿他的。

好的，真的非常感谢你们的建议~

"Dear Buyer,
Thank you for purchasing from us on Amazon, Your (item) (serial number) was delivered (Date) with signature and was as described.
I hear you are having some problems with it, I am sorry for the trouble.
Amazon policy provides for return for refund within the first 30 days, and Amazon refers support and warranty service after 30 days to the manufacturer under the terms of the factory warranty. Defective or damaged electronics can be reported up to 14 days from delivery. 
Since it has been (XX) days, Amazon does not provide any mechanism for return at this point.
I have checked, and your unit (serial) is covered by factory warranty until (date). The manufacturer's contact information is (web and mailing) and their support phone line is (phone). 
I have also looked up some suggestions for your unit here 
(FAQ, operation manual, trouble shooting links)
Hopefully (your unit can be replaced under warranty / you can have the parts ordered), and you can get back to enjoying it again quickly.
Please let me know if there in anything else we can do to help. 
Cheers 
Seller"
这是邮件模板，再说明一下亚马逊的相关政策。你不需要接受退货，如果接受了，就收取restocking fee。