The pillars are a framework for worship, not a summary of Islam, and a good deal of what Muslims do and argue about is not in them.
The most discussed omission is jihad, which some early authorities and some modern movements have described as a sixth pillar without that view ever becoming standard. The mainstream Sunni position keeps the five and treats striving, in its several senses, as an obligation of a different order rather than as part of this particular structure.
The framework is also Sunni in its formulation, and this is frequently missed. Twelver Shia Islam organises the same material differently, distinguishing the roots of religion, divine unity, divine justice, prophethood, the imamate and the resurrection, from the branches, a longer list of practices that includes prayer, fasting, pilgrimage and zakat but adds khums, a separate fifth of surplus income paid to religious authorities and to descendants of the Prophet, along with enjoining good, forbidding wrong, and prescribed loyalty and dissociation. Ismaili communities differ again. Presenting the five pillars as Islam without qualification therefore describes the majority accurately and a very substantial minority inaccurately.
What the pillars do not include at all is the greater part of Islamic law: marriage, divorce, inheritance, commerce, food, dress, and the whole apparatus of jurisprudence governing them, which is where most scholarly effort has always gone. Nor do they include the ethical material that occupies most Muslim preaching, or the devotional practices, dhikr, recitation, visiting shrines, that occupy much of Muslim religious life. The pillars are the skeleton of worship rather than the body of the religion, and Muslim scholars have consistently said so.