OP, it all depends on the 15yr old and how mature she is. Plus what the behaviour is of the kids she's looking after.
I leave my 14yr old DD in charge fairly often of my 9yr old DS and my 3yr old SDS. She is very mature for her age and very sensible. I have no problems trusting her.
What I do make sure of though is if we're far away that an adult neighbour is around so she can knock on in case of emergencies. So given your family is only 5 mins away, I think that's fine.
Is the 15yr old a sibling? If so, what I would also strongly recommend is that during the time she's in charge that you make it clear to the 11yr old that she is in charge
I've done this with my kids and it works very well. My 9yr old knows that whilst we're out, DD has full authority. That includes punishments believe it or not.
The reason for this is because I don't believe in giving responsibility without power. I know someone who left their 17yr old in "charge" but she wasn't allowed to set punishments. Result? The younger ones refused to go to bed and pretty much just ignored her.
DD also knows in no uncertain terms that power comes with responsibility. She cannot just willy nilly punish her brother. Otherwise she'll get a verbal kicking from me and grounded until the end of time.
To date, DD has never had to punish either of them. Because they know IF DD did then I'd not only uphold it, i'd punish them again!
DD babysits them a couple of times a week whilst my GF & I go to our fitness class and on the odd nights out. Quite honestly they get on better during that time than when we're around and they revert to siblings arguing over crap.