I’m afraid it is unlikely to be Sir Francis Seymour who died in 1890.
The first medal is almost certainly the 22 June 1897 Queen Victoria Diamond Jubilee Medal. The colours are very slightly off but that is likely a bit of age-discolouring. The photo also appears to have the ‘1897’ silver bar, confirming it is the 1897 Diamond Jubilee Medal. According to Wikipedia, the bar was given to those who had previously been awarded the 1887 medal so this means the man in the photo had also been awarded the 1887 Golden Jubilee Medal. Apparently the 1897 medal was awarded to, “members of the Royal Family and the court, guests at the celebrations of Queen Victoria's diamond jubilee and the soldiers and sailors that paraded that day in London”. Wikipedia states that for 1897 3,040 silver medals were awarded (in the photo the medal is clearly silver, not gold or bronze which were the other versions). So, we just need to find a General who was involved in the 1887 and 1897 Jubilee events, who was also a GCB who served in the Crimea and had the Orders of the Crown and Medjide.
Also, just to reiterate, Sir Francis Seymour died as a KCB, not a GCB. The photo has the sash and badge of a GCB.
So, whoever this portrait is of, he was still alive on 22 June 1897 and had the GCB. And he was one of the 3,040 awarded the silver version of the 1897 Diamond Jubilee Medal (having also received the 1887 version).
One other thing that might help is if the bars on the Crimea Medal painting have any text on them. Rpweedon, can you check and see if there is any text ? If there is, could you transcribe and let us know what each says. The ‘Army List’ used to detail the bars awarded for the Crimea and other campaigns so this would be very useful. Equally, a closer photo of the medals themselves would help.
Regards.
Simon