5. d3

White doesn't want to attack immediately with O-O, c3, and d4. They instead want to attack after building an impregnable fortress that offers no chances for counterplay. Though passive and harmless-looking, this move defends the e4-pawn and makes Bxc6 followed by Nxe5 a reality. Black must therefore either defend e5 or run off White's a4 bishop. Simplest is 5...b5, which removes the threat of Bxc6 but loosens Black's queenside pawns, inviting a later a4 thrust by White. Black can instead solidify their crucial e5 pawn with 5...d6, but this pins the c6 knight and restricts the f8 bishop. Finally, Black can protect e5 more actively with 5...Bc5, where 6. Bxc6 dxc6 7. Nxe5 can be met with 7...Qd4; however, other White responses, such as 6. c3, will often lead Black back to a choice between ...d6 and ...b5.

Theory table

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Wikipedia has related information at Ruy Lopez

References

• MacDonald, Neil. The Ruy Lopez, Move by Move. Gloucester, 2011