My mum lost a kidney in 2015, she's been telling me after she lost her kidney, she always sleep for only 5 and 6 hours and then wake up automatically? Is this normal for a woman who is around 47,48 years old?

what i know is older person needs lesser sleep. if she feels energetic enough then it's ok. or else she can have a noon nap

she said she feels energetic, but when it's noon sometimes she feels tired

This is quite normal, I would suggest you get her in somekind of activity in the morning or evening to build up some stamina and also to make her easier to sleep at night.

I try to convince her to jog with me in the morning, but she will always find excuses like saying she's busy. My father sometimes will take her for evening jog, as long as she sweat, its ok right?

Is she in menopause? From what I could see from my mother, she had difficulty sleeping during menopause. But it's normal for people to sleep less as they age.
She can try to get short nap during the noon (<1 hour) so she won't feel that tired.

Jogging is a hard word for people above their forties (looking at myself in the mirror now), try going trekking (FRIM or non challenging tracks) or walking in the park or somekind of low impact activity, the idea is not to sweat but to burn off the extra energy so that it will be easier to sleep.

Other than the above, I'd recommend you survey her hobbies and make that as a type of activity to move her.

nope she havent had it for a long time . i tried to tell her to sleep more and let me do the work for her, but she insist that she wanted to work . she doesnt like not working

i dont know but i think it is normal for a 45-50++ person sleep 5-6 hours a day and have afternoon nap

even all of us sometimes would want to have nap right? But too bad if we are working

Don't think it is related to the loss of kidney...

My mum slept at 12am++ and woke up before 6am every day... I would be a zombie if i did tat for continuous two days...

Is normal actually.
My mom will sleep only short hours at night and nap in the noon.
Walk around as and activity of some stretching.

there is no way that a person with only 1 kidney builds stamina.. Her body is already struggling to cope with just 1 kidney..

as people grow older, their sleeping pattern will become more similar to infants, as in less long stretch of sleeps, but more frequent naps. just my observation.

older people sleep less - true
normally when you say old ppl it referring to over 55 years old.

It not normal for people less 40 years old to sleep less unless it genetic.