Should this value be real or float?

can you split and store the significand (coefficient) and exponent in separate columns?

DECLARE @LargePrecision       TABLE
(
        [Significand]   FLOAT(53),
        [Exponent]              INT
);

INSERT INTO @LargePrecision([Significand], [Exponent])
VALUES (5.36018671369611, -20)

SELECT *,
        CASE WHEN [Exponent] > 0.0
                THEN [Significand] * POWER(10.0, [Exponent])
                ELSE [Significand] / POWER(10.0, ABS([Exponent]))
        END
FROM @LargePrecision

HOWEVER, the result continues to be out of range.