Oh and to all those saying 'go for it, it's only one day'
Yes it will be one lovely day I'm sure, but it won't solve the OP's problem that she is basically been ignoring her older DD since the toddler was born.
If your DD feels so ignored that at 5 she is "repeatedly" asking for attention it must be pretty bad because as other have said, at that age they usually just go along with things as they are, they adapt and work with the situation. They are that lovely age where they no longer need you for everything, and they don't want things done for them as they are enjoying the new found independence of not needed everything done for them.
So you have no other person who can look after your toddler? Really, nobody?
Fine, get a babysitter. The toddler will not be "upset" unless you hire really awful babysitters I'm sure the toddler will love some new attention.
Or is it just that you are as attached to the clingy toddler as she is to you and can't bare the thought of anyone else looking after her?
You need to sort out the problem of the difficult, all consuming toddler, as your DD is clearly suffering as a result of it.
I think a babysitter for every the occasional Saturday afternoon would help all of your problems hugely.
But you don't really want any of our advice do you OP.
You just want us all to tell you that YANBU. except you are.