Im looking to upgrade my processor from a Ryzen 5 2600 to a Ryzen 7 7700x. Will the stock cooling system for the 2600 be compatible with the 7700x while keeping it cool? If not which cooling system should i get for it.
Even if it is compatible, I don't think it will keep your Ryzen 7 7700X cool enough for my liking. Do you have room in your case for an All-In-One (AIO) CPU cooler, perhaps a 240mm (two-fan) radiator? If you must stick with an air-cooled CPU cooler, I like the:
The Ryzen 5 2600 box cooler (Wraith Stealth) is compatible with AM5 however it will do an extremely poor job of keeping a Ryzen 7 7700X cool, as by default it will boost up to 95°C thermal limit.
Selecting an aftermarket cooler depends on several factors such as your budget and case compatibility. How much do you want to spend and what do you have room for?
There's a lot of leeway here that can be talked about. The stock cooler for your 2600 definitely won't be able to keep your 7700X at comfortable temps, at least note for long. The 7700X has a higher watt consumption and therefore produces more heat. If you're looking for an air cooler (assuming it fits in your case) the Thermalright Peerless Assassin 120/140 is a good choice (they're a pretty good go-to cooler, I speak from experience. They're not too expensive either.)
As for liquid cooling, there's many different options. Find what appeals most to you visually, and make sure it's compatible with AM5. A 240mm cooler should be good for a 7700X processor. Keep in mind a liquid cooler/AiO will be more expensive than an air cooler.
The cooler looks good by the way.
I presume you are building a new PC from a AM4 to a AM5 Motherboard correct?
Make sure you purchase RAM Memory kit from your new Motherboard's QVL List for RAM Memory for the 7000 series processors.
The Ryzen 7 7700X has a high TDP rating of 105 watts. So you will need a CPU Cooler with a TDP of 150 watts or higher to prevent your processor from overheating.