Let $\mathrm { F } , \mathrm { F } ^ { \prime }$ be the two foci of the ellipse $\frac { x ^ { 2 } } { 4 } + y ^ { 2 } = 1$. For a point P on this ellipse satisfying $| \overrightarrow { \mathrm { OP } } + \overrightarrow { \mathrm { OF } } | = 1$, the length of segment PF is $k$. Find the value of $5k$. (Here, O is the origin.)