It could be that maybe the system is struggling. I know that CS:GO does just fine on dual-core CPUs (& unfortunately, being a laptop model that i7-5500U is only a 2C/4T CPU), but it also does better on faster CPUs (& yours is a bit on the slow side).
There's 2 possible issues that I could potentially see:
1. Not enough RAM. If you're running 32-bit Windows, there's nothing you can do, you're already at max. But if you're running 64-bit Windows, 4GB is kind of lean (especially for gaming). Even for lighter/older games, I'm not sure that 4GB is really enough RAM. That could potentially be causing the weird spikes.
2. Potential for thermal throttling. The lower TDP of laptop CPUs (& the rest of their hardware) is counterbalanced by their greater reliance on passive cooling (even those laptops with fans don't have anywhere near the airflow of even a mATX case, let alone a decent mid- or full-tower case). However, while thermal throttling can impact your performance, you don't usually see it occuring in cycles this short -- I mean, sure, you could potentially have a CPU heat up to max in a matter of seconds, but if it does it takes a long time to cool back down (minutes, many minutes).
3. Other processes running in the background are using up system resources. You'll have to use Task Manager to see what is running while gaming, & see if turning off any unnecessary processes helps out.