projectile motion with mass, find the range a missile has the position vector **_P**_ (t) = ht **_i**_ \+ t(v − 5mt) **_j**_. where m is the mass (kg) of the missile, and h/v is the horizontal/vertical speed (respectively) the missile is launched with. Using the position vector, find a range for the missile in terms of m, v and h. looked at several links, (< < (page 43)) both show different ways of showing the range but none include mass. I tried working with SUVAT equations but again, no mass. I've run out of ideas.

The formula in OP seems wrong. The correct formula is $$ \mathbf P= ht \mathbf i+t(v-\dfrac{1}{2}gt)\mathbf j $$ and $m$ has no rule, since gravitational mass and inertial mass are the same: i.e. all bodies fall in the same way, with acceleration $g=9.8 m/s^2$

So, in your case, it seems that the term $5t$ is an approximation for $\dfrac{9.8}{2}t$

The $\mathbf j$ component (vertical) is $0$ when $t(v-5t)=0$ , i.e. $t=0$ (start point) and $t=\dfrac{v}{5}$, this last time is the time whan the projectile falls and substuting it in the $i$ component (horizontal), you have the range $x= h\dfrac{v}{5}$.