Can someone explain how to work and graph this problem. f(x)=x^2+6x+5

surely your text has many examples of quadratic functions and their graphs.

I don't know what you mean by "work" this problem. To graph the function, pick a few values of x, calculate the corresponding values of f(x), and plot the points.

To get you started,
f(x) = (x+3)^2 - 4, so its vertex is at (-3,-4), and it is symmetric about the lien x = -3.

since f(0) = 5, f(-6) is also 5.

That's three points. Knowing the general shape of parabolas should enable you to sketch the graph.