Just a guess but I'd say it is a combination of some or all of the following: chain is too long (stretched with age maybe?), the cogs are worn (you can tell by the shape of the "U-shape" between the teeth, e.g., are they a "u-shaped" ?), and/or the derailleur is at the wrong angle. Even if it should never be requred to go cross-chain, the bike still should accommodate that selection because it will happen even if you know it is contraindicated and are you not trying to go there. Even so, I think you still should be able to be in your big ring and, for example, 4-5 on a 5-spd cluster.