Although the notional total load of the 5 bulbs is 300W, the low resistance of each incandescent bulb (at low filament temperature) is causing a current draw greater than that which would be drawn by a single 300W bulb (for the same overall brightness). This would be particularly so at very low light output levels.
A 1,000W dimmer should be adequately rated for this additional current.
It would do no harm to fit one of these (between Live and Neutral), to minimise mains spikes entering the unit.
http://www.maplin.co.uk/transient-suppressor-mov-499#specification