You seem to have graphed y=5x+1, whereas the given function is y=5^x + 1.
y=5^x + 1 is an EXPONENTIAL FUNCTION. y=5x+1 is a linear function and has no relevance here.
I'd suggest you FIRST graph y=5^x. If x=0, y=1; if x=1, y=5, and so on. Plot these points and draw a CURVE (not a straight line) through these points.
Next, move every one of the points you've already plotted UP by one unit. Now draw a CURVE through this set of new points. You'll then be done.