Black screen when using 4 ram sticks on brand new iMac 5K
Not all RAM is created equal. The way motherboards handle things is radically different. For example where an ASUS PC motherboard might take mismatched RAM, the iMac will not. To ensure compatibility use RAM that has the same:


Clock Speed
Voltage Requirement
Latency timings


It's best to buy identical RAM sticks. They should be the same manufacturer and the same model number. Occasionally even RAM with the same model number can have different modules on the chip. (This is very rare )

Can you update your question with details about the Manufacturer, Model number, Clock speed, voltage Requirement, and latency timings of your RAM?

UPDATE:
According to the Apple website, the RAM you bought should be compatible:
https://support.apple.com/en-us/HT201191

Might be time for the genius bar.