What would be another term for a person in their 50s and 60s other than "boomer" or "Gen-Xer"?

What would be another term for a person in their 50s and 60s other than "boomer" or "Gen-Xer"? People in their late 50s are technically baby-boomers, but "boomers" doesn't quite fit. People in their early 50s are "Gen-Xers" but that name has lost its meaning.
What could be some good names for people that are older, in general?
Elderly and even senior-citizen are just awful names!
What are some positive and non-ageist names for these people?

Solution 1:

Are you looking for another term for boomers or a term for people ages 50-60? These two categories overlap now, but they won’t as time goes on.

If the latter, neutral (albeit obscure) terms are:

• Quinquagenarian: Someone in his or her fifties.
• Sexagenarian: Someone in his or her sixties.

(Of the -genarian words, I have only seen octogenarian used “in the wild”.)

Solution 2:

There isn't going to be a term for every arbitrary range of ages, but a conventional division of a person's life would identify people between youth and agedness as middle-aged. As Collins COBUILD defines it,

Middle age is the period in your life when you are no longer young but have not yet become old. Middle age is usually considered to take place between the ages of 40 and 60.

A similar term is midlife, as in the Collins English Dictionary:

adjective
1. of or relating to middle age; of the period of life between about 40 and 60

noun
2. the period of life between about 40 and 60

These are not set figures. Some would define middle age beginning as early as 35, others might postpone it to 50; the AARP will take your dues starting at 55 while others, citing healthier living, would push seniorhood to 70 nowadays.

There is a dissonance between your stated desire to avoid ageism and your declaration that elderly and senior-citizen are "just awful" terms. If you think that any term, however clinical, which labels someone as other than young is unacceptable, then middle-aged and at midlife will not be suitable, either. Reaching midlife is associated with the midlife crisis, but like elderly or senior, these are descriptive terms, not slurs, and less patronizing than matured or golden-aged and so on and so forth.