Pedantic point: The 'grant of representation' that's required to distribute the estate of a person who died intestate (i.e. without leaving a will) isn't called 'probate'; it's referred to as 'letters of administration'.
The following people have the right to apply for letters of administration, in the order shown:
1. The spouse or civil partner of the deceased ;
2. A child of the deceased ;
3. A grandchild of the deceased ;
4. A parent of the deceased ;
5. A brother or sister of the deceased ;
6. A nephew or niece of the deceased ;
7. Another relative of the deceased.
Assuming that your grandmother wasn't married (or in a civil partnership) at the time of her death then
any of her children had/has the right to apply for leters of administration. (They could/can do so in partnership with one or more of their siblings but they're not obliged to do so; they can apply on their own).
Once someone has received letters of administration they are obliged to distribute the estate of the deceased person in accordance with the law. That would appear, in your family's circumstances, to mean sharing it between the five children of the deceased but you can check the exact rules here:
https://www.gov.uk/inherits-someone-dies-without-will
A 'grant of representation' (whether that be in the form of 'probate' or 'letters of administration') is a public document and anyone is entitled to a copy of it. If a grant has already been issued you can get a copy straight away; if not, you can enter a 'standing search', which means that you'll get a copy as soon as the grant is issued:
https://www.gov.uk/wills-probate-inheritance/searching-for-probate-records