Question Can I use CL15 and CL17 RAM together?

Technically yes but it's not recommended. Firstly you could experience instability or even BSOD's. And secondly Dell has a reputation of mixed ram incompatibilities meaning the laptop might not even boot. I'd recommend getting the same model RAM, but if you realllly need the upgrade at cheap you could give it a try.
 
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If you can replace or return the RAM you can go for it. I have mixed GSkill and Samsung RAMs without issue in my MSI laptop for over 4 years but be sure that the one you will be buying is of higher speed or of lower timings CAS. That way it will downclock. Otherwise it won't be stable as you will need to overclock it.
 
This is my current RAM type working in single channel (https://www.amazon.com/Memory-Module-Inspiron-2400MHz-PARTS-QUICK/dp/B072L6B8TP).
can I buy this one (https://www.amazon.co.uk/Crucial-CT...=1&ref_=ox_sc_act_image_1&smid=A3P5ROKL5A1OLE) and use them together in dual channel? And will there be any issues? (My Laptop is Dell Inspiron 5577 Gaming edition)

Thanks in advance guys!

If you can get the same as your RAM for about the same price its better.

The only reason I got GSkill and got to mix RAMs is that my current RAM was twice the price of GSkill.