You will find 5.Ba3!? mentioned in several books (including Lev Alburt's classic The Alekhine for the Tournament Player), but it is unlikely that your opponent has had to face it over the board. I know that almost everyone I play it against on ICC takes a very long pause at this point. White's idea is to inhibit Black's natural development: he will need some preparation to play ...c5 or ...e6. Play might return to normal Saemisch positions, but Black has to think on his own a bit and both sides have a lot of room for originality.
The Saemisch Attack was a favorite of Mikhail Tal's, and his games with it sparked my interest many years ago, so I include some classic Tal attacks with it in my notes. Tal was not always successful with the Saemisch because he often played it a bit too speculatively, as in our first game (from the first round of the 1988 National Open against an Expert level opponent) and in a 1988 simul game against Swami Shankaranda I came across online (though the opening was hardly to blame in either case).
If you like the Saemisch Attack and want to learn more, I know of a couple good resources. The best, in my view, is an article on Alekhine Defense Sidelines from Leonid's New Archive, which includes quite a few games in PGN format. Nigel Davies has also written about some of these lines in Gambiteer I (Everyman 2007), but his main focus is on Keres's preferred 3.Nc3 Nxc3 4.dxc3!? striving for speedy development rather than the central dominance that follows 4.bxc3. FM David Levin has some interesting analysis of the line 1. e4 Nf6 2. e5 Nd5 3. Nc3 e6 4. Nxd5 exd5 5. Qf3 Nc6!? -- which I mention in my analysis.
I think the Saemisch Attack makes a good fit with other dark-square systems I have written about here, including The Grand Prix with a3, The Caveman Caro-Kann, The Apocalypse Attack, The Simplified Pirc, and The Paulsen Petroff. Taken together, these practically constitute a 1.e4 repertoire, to which I might some day add the French Wing Gambit (1.e4 e6 2.Nf3 d5 3.e5 c5 4.b4!? -- also discussed in Gambiteer I), and maybe some lines of the Giuoco Piano and Two Knights Defense. And, if you like dark square systems, you might be interested in the Stonewall Attack, which is practically a repertoire in itself.