It seems absurd to put forth 5.5 to question a different rule for muslim women, because such as the aya runs, then in fact muslim women could not marry at all anybody, because where the men "are allowed" to marry women of the book they are also "allowed" to marry women believers, so , in turn, women should not be allowed to marry believing men. It is so absurd it cries out. In fact what the aya is saying is that IF men marry women believers of from the people of the book they must abide by the rules set for them, that is, pay them their retribution and not with secret dealings and all that. According to those who use this aya to impose restrictions on believing women then men would also be allowed not to pay their retribution totheir believing wives and would be allowed to seeks them unchastely. Typical obssession with male's special relationships with God.
As to what is considered to be believers in the Qur'an, I think there may be many attributions in the Qur'an not just a definition. But it is a good start with the first aya of al Baqara. At any rate I doubt that its description would be burocratic but rather a matter of the conscience and heart. No paper official paper would define a believer. So, I think that ultimately it would all revolve around the one who wants to marry's own inner belief as to the attitude if his or her pretended. Who can better know if a person believes or not than those who know her or him more closely? Unless we think the Qur'an is giving burocratic rules, which I do not think is so. The appreciation and the decision falls on the marrying person and of course, since people in love tend to be a little or much blind, sincere advice would not be out of place, but particularly, uder any circumstances, sufficient guarantees that prove the contractors good faith.
Salaam
