Pipelining requires all stages to be synchronized meaning, we have to make the delay of all stages equal to the maximum pipeline stage delay which here is $160$. We also have to add the intermediate register delay which here is $5ns$ which makes the clock period as $165ns.$
Time for execution of the first instruction $= 165* 4 = 660$ ns.
Now, in every $165$ ns, an instruction can be completed. So,
Total time for $1000$ instructions $= 660 + 999*165 = 165.495$ microseconds
Correct Answer: $C$