Your 13 year old can babysit your 5 year old legally in most places, although it also depends on your 13 year old's maturity as well as local laws and the length of time the babysitting is occurring.
If your 13 year old is mature enough and stays calm and knows how to call for help in an emergency and they have good common sense and don't get distracted easily by friends or phones and the 5 year old listens to them and behaves well then they can likely babysit the 5 year old just for awhile.
It's also a good idea for the 13 year old to take a local first aid or babysitting safety course although it's not required.
Most places don't have any strict legal age for babysitting, although you as a parent are always legally responsible for the safety of both children.
And some local child welfare agencies have guidelines that also suggest teens under age 14 should not watch young children for long hours or overnight.
If allowing your 13 year old to babysit your 5 year old, you should begin with just short trips away like 30 minutes to 60 minutes, while you remain close by.
And make sure that your 13 year old also knows basic safety as well as emergency phone numbers and how to handle any choking or fire risk or other emergencies.
And avoid leaving your 13 year old alone with your 5 year old for long stretches of time until you're entirely sure they can handle the responsibility.
I used to babysit my 5 year old brother for a few hours at age 13 and I was just fine but not all 13 year old's are ready to babysit but some are.
If you don't think your 13 year old is mature enough to babysit your 5 year old, you should hire someone else as a babysitter or if you have your 13 year old babysit your 5 year old, you could also if possible have a trusted neighbor check in on them to be sure they are okay.