Variac or not?

That amp is 45 years old. I wouldn't power it up until it was sent in for a full service and verified that it's performing correctly. The problem with old gear is that some of the parts may not be available anymore, like transistors. pop those or any other unavailable part and it's a paper weight. 

I would power it at about 70VAC for one day.  Electrolyte in electrolytic capacitors eats up dielectric (aluminum oxide) lowering breakdown voltage. Presence of voltage rebuilds this layer.  10 years is about the time I would start worrying.

+1 kijanki! Good advice!

Not.

I used to have 6 of these amps back in the day. They are well built, but on quiet passages, the fans can become annoying.
Before you do anything you may want to pop the hood and do a visual inspection to see if there are any obvious signs of leakage. If you have leaking caps, may want to replace those first.

And be careful using a variac to bring  this amp up.
There is a 10 or 20 watt power resistor in line on the AC mains to limit current inrush when the power switch is first flipped on. If you bring amp up on a varaic, you will burn out that resistor. So before bringing up on a variac, short out that resistor first with a jumper wire. If I had to guess, I would think the main filter caps may still be good, but would be suspect of all the small electrolytics on the pcb boards. Also check to make sure the fan is running when you apply power. If the fan is dead, and does not spin, don't leave the amp on for too long otherwise it may over heat the transistors. 

Can you explain why lowering supply voltage (variac) would burn out resistor in series?

I found schematic of 510M and note that "Resistor R3 must be shorted with a jumper before autotransformer is used".
In normal operation there is a time constant of about 0.3s to activate relay that shorts this resistor, but perhaps at low supply voltages relay might not turn at all. This resistor is 10 ohm in 110V version of this amp. It is hard to imagine how this resistor can burn at idle power. Assuming about 50W of idle power supply current will be about 0.5A resulting in 2.5W dissipation on this 10W resistor, but I won’t argue with manufacturer - they know better, and shorting large resistor is easy to do.

adamant40

Variac or not?

I acquired a Marantz 510M amp that had not been turned on for about 10 years.

Yes a Variac is a must, a little at a time, in 20vac mains increments over an hour to full mains volts, so to "condition (form) all the electrolytic capacitors" again, BUT!!! at the same time with meters hooked up and a scope if you have one you must monitor parameters of the amp while going up in mains voltage EG: dc offset, bias, etc etc and whatever adjustments are in the service manual

Cheers George

"Can you explain why lowering supply voltage (variac) would burn out resistor in series?"           Just thinking there may be a corollary, here:          An AC motor, connected to too long of an insufficient gauge wire/cord and the attendant voltage drop, will usually overheat, do to a higher current draw.      Will the power transformer/filter caps try to draw higher current, at charge-up, at a much lower voltage than intended?      One would think a fuse would go first.      

@rodman99999 SMPS would do that - draw more current at the lower voltage, but 510M has linear power supply. Lower supply voltage shouldn’t result in higher supply current. The issue is relay shorting this resistor, that might not activate at the lower voltage (poor design?). I still don’t see how this resistor can be damaged, unless they assume full operation (2x250W) at the lower supply voltage (not desired for conditioning of capacitors).  At idle power it should be OK, but when they say "short" I would short, just in case.