Drifted Brownian motion: hit 3 before -5

Let $X_t=mt+W_t$, where $W$ is standard Brownian motion and $m$ is a constant drift, starting from $X_0=0$.

(a) What is the probability that $X$ reaches $3$ before it reaches $-5$?

(b) Now remove the upper barrier and suppose $m>0$. What is the probability that $X$ ever reaches $-5$?

(a) $\dfrac{e^{10m}-1}{e^{10m}-e^{-6m}}$ (or $5/8$ if $m=0$); (b) $e^{-10m}$. $e^{-2mX_t}$ is a martingale, so optional stopping gives $p\,e^{-6m}+(1-p)e^{10m}=1$, which solves for $p$. For (b), let the upper barrier go to infinity: the hitting probability of $-5$ becomes $e^{-2m\cdot5}$.