If the 5 month old baby is able to sit up unassisted then yes the 5 month old baby can sit in a high chair.
Some babies are ready to sit in a high chair by 5 months old while other babies may not be ready to sit in the high chair until 6 to 7 months of age.
But if your 5 month old baby can sit up unassisted then you can safely put your 5 month old baby in the high chair.
Just be sure to properly strap the baby into the high chair and never leave the baby unattended while in the high chair even when they're strapped in.