We just bought a 05 chevy equinox 2 days ago. Last night the "service engine"light came on. My husband went to check the oil and cant find the dip stick.

Often a quart of oil consumed per 1,000 miles is considered acceptable by car manufacturers. Better check it more often, like once a month. This may be of interest to you:
https://www.carcomplaints.com/news/2018/chevy-equinox-oil-consumption-lawsuit.shtml

Service Stabilitrak, Traction Control lights ON, alone with check ...

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Chevy Equinox Eco, Traction Control and Stabilitrak Systems

? 2:39
https://www.youtube.com/watch?v=15Qj4HzpBz0

Lack of oil from the sound of it ,When checking the auto oil level start engine put handbrake on hard ,couple of bricks behind the drive wheels then drop into reverse ,now check the oil level on the autobox dipstick .If a modern vehicle with no dip stick then dealer only job to check the level

If your Oil Pressure Sending Unit went bad, it will do this

If you have a Blockage in the Oil system, it can do it

If you are low on oil, it will do this

If you have done Damage to the Engine, it can do this

If you increase your oil to 20W-50 and the light goes off, you have a worn journal or Bearing Wear

you can put it in the transmission dip stick tube with a small funnel

TURN THE IGNITION KEY TO RUN WITH THE ENGINE OFF.FULLY PRESS AND RELEASE THE ACCELERATOR PEDAL THREE TIMES WITH IN FIVE SECONDS.YOU HAVE TO DO THIS MORE THAN ONE TIME.ITS NOT GOING TO RESET FIRST TRY BUT DO THIS PROCEDURE.UNTIL THE CHANGE ENGINE OIL LIGHT WILL FLASH WHILE THE SYSTEM IS RESETTING.TURN THE KEY TO OFF.WAIT A FEW SECONDS.START CAR UP TO SEE IF CHANGE OIL LIGHT COME BACK ON.IF YES YOU HAVE TO TRY THE RESET PROCEDURE AGAIN.

No it will not. If you just bought the car. no doubt it has problems and the person you bought the car from had cleared the codes. After you have driven it a few days, the light has come on. because the engine computer (ECM) has run the tests and if a a component fails the test 2 times it will turn the light on. Sometimes a good scan tool (tech2) can tell you the "miles since cleared" and you how how many miles ago that the computer was cleared of all codes.

Hi to reset the oil life monitor
turn the key on engine off
push the gas pedal to the floor 3 TIMES WITH IN 5 SECONDS
the light will flash then go out

frist check your wires then have you aternater check ok you may have got a bad one

Well if it s like most the chevy cars trucks turn the key on and depress the gas peddal 3 times within 5 secounds and it should reset if not look in youre owners manual