The amplitude of [tex]A\sin(\omega t+\phi)[/tex] is the absolute value of [tex]A[/tex]. So first you need to condense the given function into one sine expression.
Recall that
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
so you need to choose [tex]\phi[/tex] and [tex]\omega[/tex] accordingly.
If we line up the terms of the given function with the expanded one above, we should have
[tex]2\sin(4\pi t)+5\cos(4\pi t)\implies\begin{cases}A\cos\phi=2\\A\sin\phi=5\\\omega=4\pi\end{cases}[/tex]
Now, using the Pythagorean identity,
[tex](A\sin\phi)^2+(A\cos\phi)^2=2^2+5^2\implies A^2=29\implies A=\pm\sqrt{29}[/tex]
so the amplitude is √29.
Just for completeness, we also get
[tex]\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)+n\pi[/tex]
where [tex]n[/tex] is any integer.
