If it's continuously stirring it should perk up, alas, it may take some extra time. Once it's "thick" and milky, you can pitch it as is, without crashing and decanting. A fresh starter is at its peak in viability and ready to chomp.
Once your starter has become lighter in color and milky, reproduction is fast, doubling cell count every 4-6 hours. That's the tell tale sign, and you can brew. Let it stir as long as you can, until your wort has chilled and you oxygenated/aerated it well. Then pitch the whole flask. Or transfer to a larger flask, add some extra (stronger) wort to bring gravity up to 1.040 again, and let her rip while you're brewing and chilling.
HomeBrewDad's yeast calculator shows growth to 184 billion cells from your pack in a 1 liter 1.040 starter. You'd need around 193 billion for 5 gallons of 1.055 wort, so that's close. Good oxygenation surely helps with early yeast activity, reducing lag time.
When you think about it, most packs contain 100-125 billion cells at production date, downhill from there on. They also claim one pack can inoculate a 5 gallon batch of beer (no gravity mentioned). Imagine some brewer being unaware of starters and pitches his 5 month old pack (like yours) on blind faith... With your 1 liter starter (as long as it got "thick" and milky) you're at least 4x the cell count ahead, and they're viable as can be.
When pressed for time, read up on "shaken not stirred" starters. Use a gallon jug with 1 quart of 1.040 wort and shake vigorously and often. Heck, take it to work.