EA shut down Most Wanted 2005 in 2011 due to licensing issues. Multiplayer servers were taken down, game pulled from all stores, basically just throwing the whole thing away. The only official remnant of 2005 MW's existence is this advertisement page (with no way of getting the game): https://www.ea.com/games/need-for-speed/need-for-speed-most-wanted-2005
Also, the only digital release of this game was for the Xbox 360 (now pulled from the Xbox store, obviously). All other platforms, including PC, were disc-only. So that means the only way of getting this game without pirating is to get a used disc of it. There's plenty of them on eBay for consoles, I haven't found any PC discs but there's a possibility you can find one. EA might be able to erase their digital history, but they never will be able to undo manufacturing millions of discs that will be sitting around in people's closets for decades.
Also, it's 2006 sequel (NFS Carbon) was not shut down, unlike Most Wanted, it's still available on online stores and the multiplayer servers are still up n ready in 2021. MW would be like this today if they didn't run into that stupid licensing issue.
(7/13/2021 Update: I take that Carbon "shutdown vs not" statement back. Carbon along with all 2006-2011 NFS games are shutting online services down in mid-2021 to make room for new games. But still, it was an accurate comparison of what Most Wanted would be like without the licensing problems. See this Reddit post for more info.)
TL;DR: You gotta get a used disc. EA shut the game down.
