根据搜索结果，5个元素的集合划分共有53种，具体分类如下：
划分元素为1个集合
只有一种划分方式：${{1,2,3,4,5}}$。
划分元素为2个集合
共有15种划分方式，例如：
- ${{1,2},{3,4,5}}$
- ${{1,3},{2,4,5}}$
- ${{1,4},{2,3,5}}$
- ${{1,5},{2,3,4}}$
- ${{2,3},{1,4,5}}$
- ${{2,4},{1,3,5}}$
- ${{2,5},{1,3,4}}$
- ${{3,4},{1,2,5}}$
- ${{3,5},{1,2,4}}$
- ${{4,5},{1,2,3}}$
- ${{1,2,3},{4,5}}$
- ${{1,2,4},{3,5}}$
- ${{1,2,5},{3,4}}$
- ${{1,3,4},{2,5}}$
- ${{1,3,5},{2,4}}$
- ${{1,4,5},{2,3}}$
- ${{2,3,4},{1,5}}$
- ${{2,3,5},{1,4}}$
- ${{2,4,5},{1,3}}$
- ${{3,4,5},{1,2}}$。
划分元素为3个集合
共有10种划分方式，例如：
- ${{1,2},{3},{4,5}}$
- ${{1,2},{4},{3,5}}$
- ${{1,2},{5},{3,4}}$
- ${{1,3},{2},{4,5}}$
- ${{1,3},{4},{2,5}}$
- ${{1,3},{5},{2,4}}$
- ${{1,4},{2},{3,5}}$
- ${{1,4},{3},{2,5}}$
- ${{1,4},{5},{2,3}}$
- ${{1,5},{2},{3,4}}$
- ${{1,5},{3},{2,4}}$
- ${{1,5},{4},{2,3}}$
- ${{2,3},{1,4},{5}}$
- ${{2,3},{1,5},{4}}$
- ${{2,3},{4,5},{1}}$
- ${{2,4},{1,3},{5}}$
- ${{2,4},{1,5},{3}}$
- ${{2,5},{1,3},{4}}$
- ${{2,5},{1,4},{3}}$
- ${{3,4},{1,2},{5}}$
- ${{3,4},{1,5},{2}}$
- ${{3,5},{1,2},{4}}$
- ${{3,5},{1,4},{2}}$
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