2000010601

The graph of the function $f(x)=a^x+b$ ( $a>0$, $a\ne 1$ ) has been moved $4$ units to the right and two units down. The shifted graph intersects the $x$-axis at the point $[4;0]$ and passes through the point $[8;3]$. Find $a$ and $b$ and solve the inequality $f(x)\le 5$.