Health secretary Humza Yousaf said the pay rise, which could amount to £2,400 a year for some employees, was a “demonstration of how much we value our NHS staff who have worked tirelessly to keep us safe during the course of the pandemic”.
But unions urged him to go further.
The proposed deal has also fuelled anger among police representatives, who claim their own pay negotiations have been “stonewalled”.
Calum Steele, general secretary of the Scottish Police Federation, said the offer to police officers “aggregates out at about 1.4 per cent”, which he branded “frankly insulting”.
He said: "If police officers were able to take industrial action, we would be out on strike tomorrow. That is the level of anger that exists out there just now.
"Genuinely, there are no polite words to describe just how angry the police service is.”
There are legal limits on the industrial action police can take, but Mr Steele insists there are more options “than many people believe”.
The NHS pay deal would apply to nurses, paramedics, allied health professionals and healthcare support staff, and is the largest pay rise offered to NHS workers since devolution.
But the GMB trade union said it could not recommend members accept a deal that “doesn’t sufficiently confront soaring inflation and eye-watering energy bills”.
Karen Leonard, the union’s Scotland organiser, said: “Frontline NHS services are chronically understaffed and if we want to improve this for patients, then we need to recruit and retain the people needed to deliver them, and that starts with proper value.
“In the grip of the biggest cost-of-living crisis in 40 years, we cannot recommend to our hard-pressed members the acceptance of a deal that doesn’t sufficiently confront soaring inflation and eye-watering energy bills, or a funding settlement that awards the most to the highest earners.”
The pay rise would be backdated to April 1, 2022, with the Government insisting staff could receive an additional £1,000 to £2,400 a year in their pay packets, depending on their role and experience.
Unison, Scotland’s largest health union, said it would consult members on the “below-inflation” offer.
Wilma Brown, chair of Unison’s Scottish health committee, said: “This pay offer falls well below the current level of inflation and is a real-terms pay cut for health workers.
“Our members will want to know why NHS staff on the highest pay bands will receive a rise of more than £5,500 per year while hard working domestics, porters, nursing assistants and others on the lowest bands are only deemed to be worth circa £1,000 per year.
“We have made it clear to the Scottish Government that our members will be disappointed and we will now be consulting our members on next steps. We would urge all of our members to look out for their ballot in the coming weeks.”
Julie Lamberth, chair of the Royal College of Nursing’s Scotland board, said: “This offer falls far short of our expectations of a fair pay award. Our members demonstrated their worth many times over during the pandemic.
"They have put their own health and wellbeing on the line day after day, month after month. They continue to do so as we move into remobilisation and recovery.
“We will consider the detail of the offer and how to consult members on whether it is acceptable to them. Ultimately, it will be our members who have the final say on whether or not this pay offer makes the grade.”
Mr Yousaf said: “Our NHS Agenda for Change workforce – like nursing and midwifery staff, porter staff, and therapy staff – have long had the best pay and conditions in the UK, and with today’s offer of a 5 per cent pay rise we’re demonstrating our commitment to ensuring that continues to be the case.
"It is a demonstration of how much we value our NHS staff who have worked tirelessly to keep us safe during the course of the pandemic.
“Following constructive discussions with unions and employers, we are offering the biggest single year NHS pay uplift since devolution.
“Experienced porters will receive more than £1,000 extra, while a healthcare support worker will see more than £1,200 extra. Experienced nurses will see their pay rise by more than £1,600 and an experienced advanced nurse practitioner will receive almost £2,400 more.
“In fact, as we’re building on NHS Scotland staff being the best paid in the four nations, the UK Government would need to deliver pay uplifts of between 6 per cent to 14 per cent to frontline NHS England Agenda for Change staff to catch up with pay levels in Scotland.”