So I need a new computer

This is what the guy on youtube replied to me

First of all, I don't think Newegg ships internationally. So you'll need to find equivalents at places where you can buy stuff.

(You're from Netherlands, right?) I put in "computer parts netherlands" into google and found this site that might help: http://tweakers.net/pricewatch/

Getting back to that guy's recommendations for you:
That hard drive is bad value because $15-25 more can double storage. The Samsung Spinpoint F3 and Hitachi 7k1000c can be bought at a pretty good price and give good performance for a mech. HDD.

Aftermarket CPU cooler is necessary only if you're overclocking; the retail HSF is fine if you won't. Or you can get a cooler if you're worried about a hot CPU. In that case, make sure to buy a thermal compound if it comes without one.

For RAM, just get the cheapest 4 or 6 or 8GB DDR2/DDR3 -- save the money for graphics, PSU, etc.

For case, (standard size is a Mid Tower) I recommend getting one with the front panel (audio, USB, eSATA) on top if you put your comp. on the floor. If you put it on a table/off the ground, front panel being around the middle/bottom is fine. Also, if it has no fans installed by default, you'll need to buy some (go for like $5-8 each). Usually, these have front/back fans already.

PSU: Personally, I'd go for one of OCZ's modular ones even though it has a lower overall rating on Newegg. They're sold as 500, 600, or 700 Watts -- even the 500W one should be enough for a HD5770.

Again, I haven't directly linked any sites because prices can fluctuate. So you can get good value by buying the cheapest parts (that no have red flags -- check reviews on Newegg and stay away from items with more than 20% rated @ 1-3). But use the CPU/GPU guides from Tom's Hardware to see how the CPUs/GPUs stack up.