Think I have to pay CGT but Tax Advisor says "no"

You need to be very careful with this. I claim to be rather good at Capital Gains Tax but what I know about IHT is solely what I have picked up on the way.
The links I post here will all be to the HMRC Capital Gains Manual and where they concern IHT I feel they will be right but they are no substitute to someone who really knows IHT.
HMRC uses the generalised description “Personal Representative” in its instructions and the term definitely includes Executors.
Personal Representatives can definitely be liable to Capital Gains Tax if they dispose of chargeable assets as personal representatives. This link is to the contents page “Death and Personal Representatives.
http://www.hmrc.gov.uk/manuals/cg2manual/CG30200c.htm
The general principle is that when someone dies he leaves an estate which passes to the personal representatives at its open market value at the date of death.
The personal representatives are then responsible for paying out what has to be paid out, debts, funeral expenses, IHT etc. In a relatively straightforward case they are then required to distribute the estate to the beneficiaries. If they have to sell capital assets to fulfil their obligations there is definitely a potential Capital Gain chargeable to CGT.
Whilst you have said that IHT doesn’t come into your case a very common example is that the personal representatives have to sell a property in order to pay the IHT before they can distribute the residue to the beneficiaries.
If the estate was liable to IHT then what Jimmy230 said would, in my opinion, be nearly right.
Personal representatives who sell capital assets can revise the IHT Return to replace the original Probate Value with the proceeds of sale but there are rules and one of them is that the sale must take place within 4 years of the death.
http://www.hmrc.gov.uk/manuals/cg2manual/CG32390.htm
You have said that the sale took place 5 years after your mum’s death. Therefore you don’t qualify (Reminder, this comes from HMRC instructions on CGT not IHT so check it carefully.)
I think that the situation your are in is that your mum left a property which someone has valued at £80,000 at the time of her death and whilst the IHT office has accepted that her estate was not liable to IHT they have not actually formally accepted that valuation.
The executors have subsequently sold the property for £185,000.
There is definitely a Capital Gain chargeable to tax.
Then you have to look at whether the executors sold the property in their own right, in which case they are chargeable as executors, or whether they sold it as bare trustees of the beneficiaries. In which case the beneficiaries are deemed to have acquired the property at the date of your mum’s death and sold it when it was sold.
The beneficiaries are the Trust and if you are also a trustee then I think you really need to take some time to come to terms with the legal reality that for tax purposes you are at least 3 separate persons
You, the individual
You, the executor
You, the trustee.
Each has their own legal responsibility and you could be punished if you get it wrong.

In my days as a taxman I would certainly take this on and expect to win hands down but most of the issues concern legal matters and the tax consequences follow from them.
I just don’t buy the idea that all this can be swept into your mum’s estate and I think there is a real danger that there is a substantial tax liability floating around waiting to land on somebody.

You obviously have similar misgivings and, in many ways I think that if your tax advisor (is he qualified?) and the solicitor have not been able to explain the situation to you in words you can understand you have a real problem.
It’s probably too complicated to handle here but I think you need to move on to a solicitor and/or tax advisor who can convince you that they know what they are doing.

Excellent post Jimmo.

I would agree that the OP has received incorrect advice and the increased value of the property is subject to CGT and not IHT.

IHT is based on the value of the estate at the date of death (or the probate value). If during the course of the administration, the personal representatives discover further assets, or for any reason the value of the initial valuation alters (ie its value was estimated originally on the estate account), HMRC must be notified and a corrective account may need to be filed, and where applicable additional IHT must be paid (or where overvalued, then reclaimed).

In the absence of a clearance certificate from HMRC, there remains the possibility that HMRC will query whether a valuation of the asset at the date of death is correct - and so before distributing the estate, the PRs would be wise to obtain one to be sure that no further IHT demands will be made of them.

However once it is clear what the exact value of the estate was upon death, then any gain in the value of assets forming part of the estate will be subject to CGT. The PRs are liable for paying this and the base cost of such an asset is its value at the deceased's death, as agreed with HMRC.

I am not a CGT expert, but from my understanding PRs paid CGT at 40%, and taper relief was available. They have an annual allowance, the same as any individual for the same tax year that the deceased died, and the following two years. After that they have no annual allowance, unless as Jimmo correctly says they qualify in another capacity, e.g as trustees.

Any gain in the value of the deceased's family home is not exempt from CGT simply because it was the deceased's main residence. Further, if the sale price is substantially higher than the probate value, HMRC could seek to increase the market value at the date of death (with a view to extracting more IHT) and any capital gains tax would be calculated by reference to the revised probate value - though an upward revision in the probate value could work to the advantage on an estate that was not in any case subject to IHT.

I would really echo the advice provided from Jimmo and seek out the advice from someone clued up in this area as I fear that a nasty tax burden could be falling on your shoulders otherwise. Remember that the penalties can be quite severe for PRs who have underpaid any tax due and you really don't need the hassles of having to later try and prove that your losses were caused by the incorrect advice provided by your advisers.