I am changing my rear derailleur and cogs. I purchased a new 10 speed chain. These are the parts

Chain -CN6600 10s 116L
cogs - CS6600 12-23 10s
Derailleur -DR6600

The front chain ring is 105 5500. A52,A42,A30

Do I start taking chain links off?

When I'm on the biggest cog in the front the tension is ok but when I go to the smaller cog there is no tension on the chain.

Did I install it wrong?