Using the intermediate value theorem, determine, it possible, whether the function $\mathrm{t}$ has at least one real zero between a and $b$. \[ f(x)=x^{3}+2 x^{2}-5 x-4 ; a=-5, b=-3 \]

Step 1 ：Given the function \(f(x) = x^{3} + 2x^{2} - 5x - 4\) and the interval \(a = -5\) and \(b = -3\).

Step 2 ：According to the Intermediate Value Theorem, if a function is continuous on a closed interval [a, b], then it takes on every value between f(a) and f(b) at some point within the interval.

Step 3 ：First, we need to evaluate the function at a and b. If the function values at a and b have different signs, then there is at least one zero between a and b.

Step 4 ：Calculate \(f(a) = f(-5) = -54\) and \(f(b) = f(-3) = 2\).

Step 5 ：Since \(f(a)\) and \(f(b)\) have different signs (\(f(a)\) is negative and \(f(b)\) is positive), there must be at least one zero of the function in the interval (a, b) according to the Intermediate Value Theorem.

Step 6 ：\(\boxed{\text{Final Answer: There is at least one real zero between a and b.}}\)