I don't think that White has too much trouble generating enough compensation for the pawn against 5...Bg4 or 5...e6, but 5...Bf5, 5...g6 and 5...c6 all pose White some theoretical problems. White always gets some attacking chances though.
After 5...Bg4 Black threatens to undermine White's d4-pawn and continue developing actively, so White typically forces the issue with 6.h3, whereupon Black can retreat the bishop with 6...Bh5 and 7.g4 Bg6 8.Ne5 follows. The most critical continuation is then probably 8...e6 9.Bg2 c6, where Black sets up a solid formation similar to the Caro-Kann Defence.
Here Black's idea is to meet 10.h4 (threatening to trap the bishop on g6) with 10...Bb4, pinning the knight on c3 and preparing kingside castling. After 11.0-0 Nbd7 I recommend that White respond to the challenge on the knight on e5 with 12.Nxg6 rather than 12.Qe2. I also think 10.Rf1!? is a good option for White, bringing a rook to the f-file immediately and intending queenside castling, which will give White more scope to push the g and h-pawns without leaving the white king exposed. Christoph Scheerer didn't treat this line well in his book, referring to a game where White played poorly and drifted into a losing position.
Traditionally, the main line sees Black chop off the f3-knight with 6...Bxf3 7.Qxf3 c6.
Here the traditional main line is 8.Be3, followed by a slow kingside build-up, but a few sources (notably "ArKheiN" at the Chesspublishing.com forum, and Christoph Scheerer in his book) have persuaded me that the more daring 8.g4!? is the way for White to go. The idea is, instead of quietly completing development, to chase the f6-knight away with g4-g5 and blast through down the f-file, even at the cost of a second pawn. White appears easily able to get enough compensation for the pawn if Black doesn't take on d4, so 8...Qxd4 is critical, but it appears that White can get two pawns' worth of compensation. This line has proved a lot of fun at the local chess club. 8...Qxd4 9.Be3 Qe5 10.0-0-0 e6 11.g5 Nd5? 12.Nxd5 cxd5 13.Bf4 Qe4 14.Qxe4! dxe4 15.Bxb8 Rxb8? 16.Bb5+ is one trap that is easy for Black to fall into. Black plays natural moves and swaps the queens off, but ends up falling for a mating attack.
Of course, this doesn't mean that the BDG is theoretically good for White, because Black has three options that are rather more critical than 5...Bg4, but in practice, 5...Bg4 is the most popular of Black's fifth-move options so if you play this opening frequently with White you will regularly face it. I will shortly write brief articles on Black's other fifth-move options, but for now, those interested in seeing my in-depth coverage of the other lines can check out the links provided above.