Wanting an IF function within a LOOKUP function?

[RainbowSensation]

Hi there, I am just seeking some help - I get a bit confused with functions sometimes.
I have this lookup function in cell J5 which works as intended - it looks up the second worksheet for the last entry of Bob's Bakery and the returns the associated date.
However some places won't have anything in the business column if they aren't a business - I'd like to try match the business column and return the value, but then if the business column is empty for it to search the name column and try and return the data associated with that.

b0fe45dc25f98f4abdc5d1d37b04c3af.png
5af55ff7900a43d81f68335816e763d6.png

Sorry if I didn't word it very clearly haha.
Any help would be appreciated.

[Phuocam]

Maybe like this:

=IFERROR(LOOKUP(2;1/('Cleaning Record'!B:B=Sheet1!A5);'Cleaning Record'!B:B);
LOOKUP(2;1/('Cleaning Record'!B:B=Sheet1!B5);'Cleaning Record'!B:B))