All the Chinese elms, sometimes called lacebark elms, are resistant to disease. Anytime from fall to late winter it great for planting although container grown trees can be planted anytime of the year. By planting in the cool season however the tree has maximum time to get roots established before the onset of the hot summer season.
Your tree that died after 5 years most likely did not die from a problem with the top but most likely from a problem in the roots (soggy soil, root damage, root rots, herbicide injury, etc.).
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