Let $S_{0}(t) = (1-\frac{t}{105})^{1/5}$ be the survival function of a newborn. What is the median future lifetime at age $50$? So $S_{50}(t) = \frac{S_{0}(50+t)}{S_{0}(50)} = \frac{\left(1-\frac{50+t}{105}\right)^{1/5}}{ \left(1-\frac{50}{105}\right)^{1/5}}$
The median future lifetime would be the value of $s$ such that $ \int_{0}^{s} \frac{\left(1-\frac{50+t}{105}\right)^{1/5}}{ \left(1-\frac{50}{105}\right)^{1/5}} \ dt = 0.5$
Is that correct?