Is this achievable or unrealistic?

Im 23 and I’ve just started a new job where I’m on 40k a year. The work is guaranteed till at least 2060 so theres no risk of work running out. There’s unlimited guaranteed overtime whenever we want it. I work 3 on 4 off but have been doing one overtime a week doing 4 on 3 off which brings my yearly salary up to 60k+ (3.5k per month, 5k per month after overtime)

I’m looking to buy a house. I have about 4k in savings. I’m only looking for something modest for maybe 70-80k over 15 years. Not gonna be a forever home, but a home for now while partner isn’t working/at university so will be just my income. This would be my first property so I’d like to think I qualify for a first time buyer scheme so would only need 5% rather than 10% deposit.

Going off basic salary before overtime, outgoings per month are around £800 which leaves about 1.8k per month, and general living, food, spending is around £800 so £1000 extra per month.

70k over 15 years at 5% is £550 a month assuming interest rate doesn’t change. Leaving me with £450 extra for utility bills and potentially work on updating some things (and more with overtime)

I know I’ll need solicitator fees, conveyancer fees, etc and this I estimate will be around 2.5k

Is there anything I’ve not mentioned that should be taken into consideration, or is this a reasonable plan?