Disk covering problem $r(5)$

The smallest value $r(5)$ such that $5$ disks of radius $r(5)$ can be arranged to cover the unit disk.

Value: ${\approx}0.609382$

Updates

Upper bound: ${\approx}0.609382$
Reference unknown
[via Circles Covering Circles, Erich Friedman]
1983 Lower bound: ${\approx}0.609382$
Károly Bezdek in 1983
[via Circles Covering Circles, Erich Friedman]