According to Faraday's Law of Induction, the magnitude of the induced electromotive force ($|\varepsilon|$) is equal to the rate of change of magnetic flux ($\phi$) with respect to time ($t$).

1. Formula: $|\varepsilon| = \left| \frac{d\phi}{dt} \right|$
2. Given Flux: $\phi = 2t^3 + 4t^2 + 2t + 5$
3. Differentiation: $\frac{d\phi}{dt} = \frac{d}{dt}(2t^3 + 4t^2 + 2t + 5)$ $\frac{d\phi}{dt} = 6t^2 + 8t + 2$
4. Calculation at t = 5 s: $|\varepsilon|_{t=5} = 6(5)^2 + 8(5) + 2$ $|\varepsilon|_{t=5} = 6(25) + 40 + 2$ $|\varepsilon|_{t=5} = 150 + 40 + 2 = 192 \text{ V}$