5. Thanks for your confidence and support, and we will be always at your service.
謝謝您的信任和支持，我們將熱忱為您服務。
還能這樣說：
We appreciate your confidence and support and we will service you in a good way.
We provide satisfactory service for our customers to express our gratitude for your confidence and support.
應用解析：
come to one's support 來支持某人；
give support to 支持，支援；
in support of 幫助，為……辯護證明

6. our object is to further cement trade relations with you.
我們的宗旨是進一步鞏固與你們的貿易關系。
還能這樣說：
To further strengthen the trade relationship with you is our purpose.
We aim to consolidate the business connections with you.
應用解析：
cement的意思是：水泥；膠結材料；（團結的）紐帶；粘結，鞏固。

7. I hope that we can expand our business to abroad.
我希望能把業務做到國外。
還能這樣說：
I hope we can sell a lot of products overseas.
I wish that we can run business at abroad.

8. I have to write a summary of our monthly report.
我不得不寫一下本月匯報總結。
還能這樣說：
I have to record a summary of the monthly report.
I need to write a monthly report.
應用解析：
draw up a report 起草報告；
present a report 呈遞報告