What's broken on your E53 today!
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Proper fix. Drill out the melted plastic rivets. Shim out to original height and use self tapping screws to attach the metal frame.

Design defect the 21w high filament gets hot enough to melt the plastic and the spring pressure pushes the contact away from the bulb adding resistance that causes more heat and faster melting.

It doesn't hurt to put some silver solder on the contact points but that doesn't eliminate the root cause.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)