intersection of 3 Values

i have a sheet1 contain a table of information , and sheet2 the value and Result what i want to search in sheet1 , i need a macro to search values of column E sheet2 with 2nd Row of sheet1 , in the same time the value of Cell A5 in sheet2 with 1st Row of sheet1 , when these two condition exist in the same column of sheet1 i want to find the intersect with match the value of column T sheet2 with Column A sheet1. put the Result in Column U sheet2 , and Column V sheet2 equal the offset of this result ( intersection ) to the right

please see attached file as Example

is there any one can help me ?
i just want to search column that match 2 values in 2 rows ( row1 and row2 ) , then find 3rd value by Rows and get the value of intersection.
then get the value beside this intersection one column to the right .

please see attched file above

thanks in advance

Dear Mr. jaslake ,
when i select the Name from a drop Down list in cell A5 , and click the Button , it gave me Run-time error'438' : object doesn't suppot this property or method , and fill yellow the line in the code : Rng.RemoveDuplicates Columns:=Rng.Column, Header:=xlNo .
what does it mean ?
why you type each name of student many times in the sheet lists and not one time ?

Note : the Result in the yellow cells are exactly the Result what i want.

thand for your attention

also i need :

if the No. of Exam No. in sheet2 column T not exist in Sheet1 Column A , in need the result to be the first greater than it . ie. if the Exam No. of sheet2 column T is 3 , and this No. is not exist in Sheet1 column A , want the code to search for the first greater in column A that is mean No. 4 ( or any first greater ie if No. 4 , 5 , 6 and 7 not exist in sheet1 column A , so the first greater than No. 3 is No. 8 ) .

please see attached file again . and help me .

Thanks

also i need :

if the No. of Exam No. in sheet2 column T not exist in Sheet1 Column A , in need the result to be the first greater than it . ie. if the Exam No. of sheet2 column T is 3 , and this No. is not exist in Sheet1 column A , want the code to search for the first greater in column A that is mean No. 4 ( or any first greater ie if No. 4 , 5 , 6 and 7 not exist in sheet1 column A , so the first greater than No. 3 is No. 8 ) .

please see attached file again . and help me .

Thanks

dear Mr.jaslake :
thanks for your attention , the code in the last workbook you sent is working perfect , but when i copy the code to my original workbook it gives me this message Compile error: Sub or Function Not defined ), and mark the line : f = getclosest(ws1.Range(("A3"), ws1.Range("A" & Rows.Count).End(xlUp)), myExam).
i didn't understand it , please help me .

thanks

Thanks a lot Mr. jaslake , the code is working very perfect .
i have just one thing , how can i edit and fix the Rng1 to be just equal to the cell L3 , and not to be all the Rows in column E (Set Rng1 = .Range(.Cells(3, 5), .Cells(.Rows.Count, 5).End(xlUp))
thanks in advance

just only cell L3 , instead of all cell of column E

thanks Mr jaslake for your help , the macro is working perfect .