Hi SlatkaMala,
I suffer from this too. I like (a little) caffeine so sometimes a small afternoon cup of black tea helps me to have a little boost. But lately it just got too bad so I went the medication route and I'm hoping it will help... Are you taking any medication now? The reason I ask is that some have lethargy as a side effect.
I guess if the exhaustion is around cleaning I will say to myself "I am going to put only 3 items of clothing away." Or, "I will was only 2 dishes." After that I usually will wash just a couple more or put maybe 5 items of clothing away. But I have to say the exhaustion problem with depression is certainly hard. So I'm mostly focused on trying to treat that, I guess.
Sending many supportive thoughts your way...

E