Looking to be able to select specific rows and columns and display only those selections

I'm trying to set up a data analysis worksheet that has specific row and column headings. I want to be able to select the row/column and display that on a separate sheet, but only the selected value of each row and column.

For example, if I have rows 1,2 ,3, 4, 5 and columns a,b,c,d,e, I want to be able to select row 1,3,4 and column c,d,e and display just those values on a separate linked sheet. I would be able to change the rows/columns selected.
Originally i tried this with checkboxes, but ran into a lot of trouble with embedding them into the worksheet and having them reference an entire row/column. I also tried the pivot table, but it was very clunky.

Any insight is greatly appreciated.

CJ