hiding conditional format when activating cell is empty

Sorry for that title but this is difficult to explain. I have uploaded a sample workbook to show it better.
I'm refering to the small blue info box on the right of sheet 1 and also the duplicate on sheet 2.
The left side of the box is where I will insert qualification, and the left mostly are the expiry dates. The details are then replicated in other worksheets as in sheet 2.
I have conditionally formatted column 'X' to 'ALERT' when the date is within 60 days of the expiry date (that bit works OK)
but
if the master info block (sheet 1) doesn't have a date in it down the righthand side, two things happen
1. , the subseqeunt box on the following sheet show the date 0 January 1901 with the 'Alert' flag showing alongside it.
2. The 'Alert' warning flag shows on the master info block (sheet 1)
I would like to hide the 'Alert' and the 1901 date if possible when there is no date in the righthand column.
I hope you can follow this pathetic attempt at explaining the problem.
Additinally for some unknown reason a '0' as appeared in column 'U' on sheet two if you could also advise on that.
Thank you very much

Select H5:H12 in 2nd sheet and then go to conditional formatting. Erase everything there and use this one

=AND(NOT($E5=""),$F5-60<TODAY())

WB is also attached
Is that what you're looking for???..

HTH

Thanks HTH, In answer to your question, yes that's what I'm looking for, but I couldn't get it to work on my copy so I looked at how you did it and have cocked it up a bit (sheet 2 H11) I'm not sure what I've done but it won't work. I tried entering your formula into the conditional format and pulling it down from the others above, but failed, There are quite a few other headings and dates to go in the box so I would like to be able to understand what I've done wrong.
I don't know how you got rid of the '0' in column 'U' but thanks again for that.

My problems are still on sheet one with the 'Alert' flag still showing if there is no date in it, but what you have achieved in such a short time on sheet two is great I have upload the two sheets you have worked on to show you how I cocked it up(sorry) I have attached the cocked up version

Having got up early this morning with a fresh mind, I have made some progress, I still don't understand what this means exactly and my book doesn't help me much in deciphering it. =AND(NOT($E5=""),$F5-60<TODAY()) I have got it in place though.

I have managed to resolve the problem of the date 00 January 1900 that appears in Coloumn F sheet 2, when column V7 to 17 in sheet 1 are left empty.
I did this by setting up a conditional format to change the text to the bacground colour if it saw a date prior to 01 January 1900. This seems to do the job OK. but I really wanted it to be blank like its master on sheet 1.
I still have the problem though of my alert boxes, Is there a formula that would keep them from activating, until the cells are populated. I have tried lots of formulas, but I don't really understand them that well yet, so haven't got there yet.
I have attached the workbook sample
Thanks

AND(NOT($E5="", is the same as
AND($E5<>"",
for your other bit
just use in F7
=IF(Sheet1!V$7="","",Sheet1!V$7) no need for cond.format then

<> means does not equal so e5<>"" means if e5 isn't blank
what is this suppose to do?
=" Alert "&TEXT(V7,)?