In order to find the exponential function, let's use the model:
[tex]y=a\cdot b^x[/tex]Then, to find the values of a and b, let's use the first two points of the table:
[tex]\begin{gathered} x=0,y=5\colon \\ 5=a\cdot b^0\to a=5 \\ \\ x=1,y=15\colon \\ 15=5\cdot b^1 \\ b=\frac{15}{5}=3 \end{gathered}[/tex]So our function is:
[tex]y=5\cdot3^x[/tex]