I'm not sure I understand what you're asking exactly, but I guess you could say it doesn't. It's important to remember the "bill of rights" is really the "bill of government restrictions", not "bill of fundamental human rights". I guess that, unlike the right against self-incrimination, spousal privilege wasn't deemed fundamentally necessary for preventing the government from forcing testimony, so that's probably why it wasn't put there in the fifth amendment. I can only speculate as to the reasoning, but I imagine it might be as follows:
With self-incrimination, if the government decides to force testimony from you (which inevitably implies a guilty confession), you'll get punished one way or another regardless of what you say (which apparently historically meant choosing between torture and death). This means two things: (1) innocent people will get punished either way (which is obviously the opposite of what you want), and (2) guilty people won't have any incentive to tell the truth either (which is also not what you want either)—they'll instead have incentive to say whatever will minimize their punishment, which is determined by the government, not by the truth. So it's pretty much entirely a lose-lose situation, and not something that'll make a justice system (whom you're charging with the task of finding the truth) achieve its goal. Spousal testimony, on the other hand, is entirely different in that respect: as far as the relationship between you and the government is concerned (which is, recall, what the goal of the bill of rights was—again, it wasn't written as a manifesto on human rights), you actually have a huge incentive to tell the truth here, because you don't get punished by the government for providing guilty testimony against your spouse. Same exactly thing happens when you're provided immunity: you don't get punished, and therefore society gets to extract the truth out of you, with decent confidence that it'll get what it's looking for. Therefore, as far as the constitution being concerned, spousal privilege probably didn't need to be written in there, because the right against self-incrimination already sufficiently achieved its restriction and goal.
With self-incrimination, if the government decides to force testimony from you (which inevitably implies a guilty confession), you'll get punished one way or another regardless of what you say (which apparently historically meant choosing between torture and death). This means two things: (1) innocent people will get punished either way (which is obviously the opposite of what you want), and (2) guilty people won't have any incentive to tell the truth either (which is also not what you want either)—they'll instead have incentive to say whatever will minimize their punishment, which is determined by the government, not by the truth. So it's pretty much entirely a lose-lose situation, and not something that'll make a justice system (whom you're charging with the task of finding the truth) achieve its goal. Spousal testimony, on the other hand, is entirely different in that respect: as far as the relationship between you and the government is concerned (which is, recall, what the goal of the bill of rights was—again, it wasn't written as a manifesto on human rights), you actually have a huge incentive to tell the truth here, because you don't get punished by the government for providing guilty testimony against your spouse. Same exactly thing happens when you're provided immunity: you don't get punished, and therefore society gets to extract the truth out of you, with decent confidence that it'll get what it's looking for. Therefore, as far as the constitution being concerned, spousal privilege probably didn't need to be written in there, because the right against self-incrimination already sufficiently achieved its restriction and goal.