Bird identification: song two low, two high, five short
Best guess is that the bird is a Song Sparrow, Melospiza melodia. Cornell Lab of Ornithology has a good website for basic facts about birds. Here is the account for Song Sparrow. There is a sample of typical song, but there can occasionally be some variety.

The song is kind of complex and the recording you linked to seems to garble or not capture some of the song, but the changes in phrases throughout the duration seem to match as does the pitch of most of the phrases.