LSE definitely doesn't have one of the top 5 econ departments in the world- top 15 at best. I can't see anyone ranking LSE ahead of NYU, Northwestern, Yale, Columbia, Berkely etc. all top 10 depts. LSE as a dept would be around the level of Duke(top 15ish), it's still very good but definitely not top 5(while it isn't a good indicator and has several flaws, REPEC puts LSE at 28). In terms of a PhD program it's probably a bit like Cornell in that it punches below it's weight when it comes to placements etc. It is the best department in Europe overall, but there are better places for your PhD in Europe if you have certain fields in mind- UCL for microeconometrics and theory, UPF for Macro etc.