Can we complete the $5 \times 5$ grid by using $1 \times 2$ rectangles?

Can we complete the $5 \times 5$ grid by using $1 \times 2$ rectangles?

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Adding $1 \times 2$ tiles will only cover an even amount of squares if they are not allowed to overlap. The grid has $25$ tiles which is odd. So no it cannot be done.
To improve the question it is best that you show working. In this case perhaps how many tiles did you lay before coming unstuck?
How many of the small rectangles would you need?