A child should be able to take a shower by themselves by age 5 to 6 years old.
However a child may need supervised somewhat when taking a shower by themselves even at age 5 to 7 years old to ensure they actually take a shower and get clean.
I had a 7 year old boy who I had to make sure he got clean because he would sometimes dirty a towel and then turn the shower on and let it run for awhile.
Then he would just change his clothes and never got into the shower at all.
Kids do that sometimes so I had to give my 7 year old a shower to make sure he got clean because he would not do it if I didn't wash him down myself.