What do you exactly mean with "...at the other end of VLAN 25"?
If, at the other end of the point-to-point link that start from port 5 of your Switch, there is a port that belongs to a different Switch...then you need to configure that remote port exactly like (from the point of view of Untagged/Tagged VLANs and of Port Type - better to use "Trunk" type) you did on the local one of your first Switch. Basically this will define a Trunk type with VLAN 1 Untagged and VLAN 25 Tagged, logical trunk port's type should be set of type "Trunk" (not Hybrid).
Doing so and so permitting VLAN 25 (Tagged) on that Trunk any hosts on VLAN 1 will be able to ping any hosts on VLAN 1 on the other's end (2nd Switch) and vice-versa, the same will be valid for any hosts on VLAN 5 25 (Edit) on the 1st or 2nd Switch.