Is there a word for the feeling of growing old?

Question

Is there a word for the feeling of growing old? Or the feeling of becoming more mature?

Something that describes the way you feel when you wake up in the morning and notice how much has changed:

When the man woke up, he saw his wife, his daughter in the crib, and finally, himself in the mirror, and felt [feeling] as he pondered how fast time had gone by.

It's not really yearning for the past, though, so it's not quite nostalgia. It's a bit more like the way someone would feel when they say: "the days are long but the years are short."

Answer 1

The process of growing old from either an internal perspective (i.e. your own), or external perspective (in the eyes of others) is known as senescence.

From Dictionary.com:

senescence

growing old; aging

Or, a more colorful and richer definition from Vocabulary.com which aligns with the feelings you describe in your question:

senescence

Do your stiff knees make it harder and harder to get out of that cozy chair? It may be that senescence is at work, meaning you’re getting older.

Senescence is a fancy way to describe the process of aging. If you don’t want to admit straight out that old age made you lose that tango contest, blame it on senescence — it sounds mysterious and exciting. Senescence is sometimes used in a scientific context to describe cells in your body that can no longer grow and divide, which can affect your ability to dance like you did when you were 20.

Answer 2

I like ageing to describe this feeling. vocabulary.com

the organic process of growing older and showing the effects of increasing age

As in:

I need help to cope with the demands of my ageing body.