how to correctly assign to these variables

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True for older VHDL, but VHDL-1993 onwards will correctly convert the hex string to a std_logic_vector without needing to convert it explicitly. Not that yours is wrong, just two ways to skin this cat :). Personally I prefer the cleaner look of the direct assignment without lots of explicit type conversions.

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the x"12345" is just that, a hex string, its not an integer or anything, its just a string of bits.

The OP started talking about integers, which is not a hex string, and thus requires the type conversion.