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here we have a five of two in the key of D major. As in the first example, the first chord is the dominant of the second chord. In this case the sixth scale degree is altered from minor (what it would be naturally) to major to increase the sound of resolution to the second chord, in this case the second scale degree E minor.

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Here we see a five of five in the key of C major and a five of two in D major. in the first visual, you can see how the altered chord is the second scale degree. In the initial key, the chord would be D minor, however because it is a secondary dominant, the F is raised a semitone and thus becomes major, and consequently the fifth of G.

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the third of the supertonic chord is the sixth scale degree of the initial key's relative minor. If we go to the relative minor with the five of five chord, we now have a dorian mode. While it would likely be considered simple modal mixture, i feel that its important to recognize these connections because it helps for further understanding and can create some fun ideas for composing.

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Additionally, I've found that some secondary dominants help for songs in modes. For example, the five of five secondary dominant is primarily used to modulate to the dominant of the initial key or at least create some resolution to the dominant. However, the five of five alters the supertonic, which alters primarily the third of the chord changing the chord from minor to major. Now what's the big deal, well I'll tell you

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Secondary dominants are just from a long list of things that make music better. Their main function is to provide a quick little feeling a resolution to a chord other than the tonic to keep the ear interested. Additionally they are great for actually modulating to a new key.

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secondary dominants are the dominant chord built off of a chord from the initial key signature. the secondary dominants are not in the initial key signature and will always require accidentals. Even the elusive five of four secondary dominant has an accidental even though it will only be seen through the seventh of the chord.

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In short, if the first chord is the dominant of the second chord, it is a secondary dominant. the first chord will always resolve to the second chord as a general rule of thumb and will always be major.

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look for naturals or sharps, thats literally it. Im mainly kidding, however there will always be a sharp or natural due to the nature of secondary dominants. After you find a chord that doesn't fall into the natural key, look to the chord right after it. now here's the part thats hard to word. Acting as if the second chord is the "new key," if the first initial chord is the dominant of the "new key" then is it a secondary dominant